A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators
riginally developed within the realm of mathematical physics, integral transformations have transcended their origins and now find wide application across various mathematical domains. Among these applications, the construction and analysis of special polynomials benefit significantly from the eluci...
- Autores:
-
Zayed, Mohra
Wani, Shahid Ahmad
Oros, Georgia Irina
Ramírez, William
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2024
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/14123
- Acceso en línea:
- https://hdl.handle.net/11323/14123
https://repositorio.cuc.edu.co/
- Palabra clave:
- Applications
Eulers’ integral
Explicit form
Fractional operators
Multivariable special polynomials
Operational connection
- Rights
- openAccess
- License
- Atribución 4.0 Internacional (CC BY 4.0)
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A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators |
| title |
A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators |
| spellingShingle |
A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators Applications Eulers’ integral Explicit form Fractional operators Multivariable special polynomials Operational connection |
| title_short |
A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators |
| title_full |
A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators |
| title_fullStr |
A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators |
| title_full_unstemmed |
A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators |
| title_sort |
A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators |
| dc.creator.fl_str_mv |
Zayed, Mohra Wani, Shahid Ahmad Oros, Georgia Irina Ramírez, William |
| dc.contributor.author.none.fl_str_mv |
Zayed, Mohra Wani, Shahid Ahmad Oros, Georgia Irina Ramírez, William |
| dc.subject.proposal.eng.fl_str_mv |
Applications Eulers’ integral Explicit form Fractional operators Multivariable special polynomials Operational connection |
| topic |
Applications Eulers’ integral Explicit form Fractional operators Multivariable special polynomials Operational connection |
| description |
riginally developed within the realm of mathematical physics, integral transformations have transcended their origins and now find wide application across various mathematical domains. Among these applications, the construction and analysis of special polynomials benefit significantly from the elucidation of generating expressions, operational principles, and other distinctive properties. This study delves into a pioneering exploration of an extended lineage of Frobenius-Euler polynomials belonging to the Hermite-Apostol type, incorporating multivariable variables through fractional operators. Motivated by the exigencies of contemporary engineering challenges, the research endeavors to uncover the operational rules and establishing connections inherent within these extended polynomials. In doing so, it seeks to chart a course towards harnessing these mathematical constructs within diverse engineering contexts, where their unique attributes hold the potential for yielding profound insights. The study deduces operational rules for this generalized family, facilitating the establishment of generating connections and the identification of recurrence relations. Furthermore, it showcases compelling applications, demonstrating how these derived polynomials may offer meaningful solutions within specific engineering scenarios. |
| publishDate |
2024 |
| dc.date.issued.none.fl_str_mv |
2024-05-09 |
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2025-04-07T20:22:58Z |
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2025-04-07T20:22:58Z |
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Artículo de revista |
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Mohra Zayed, Shahid Ahmad Wani, Georgia Irina Oros, William Ramŕez. A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators[J]. AIMS Mathematics, 2024, 9(6): 16297-16312. doi: 10.3934/math.2024789 |
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2473-6988 |
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https://hdl.handle.net/11323/14123 |
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10.3934/math.2024789 |
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Corporación Universidad de la Costa |
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REDICUC - Repositorio CUC |
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https://repositorio.cuc.edu.co/ |
| identifier_str_mv |
Mohra Zayed, Shahid Ahmad Wani, Georgia Irina Oros, William Ramŕez. A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators[J]. AIMS Mathematics, 2024, 9(6): 16297-16312. doi: 10.3934/math.2024789 2473-6988 10.3934/math.2024789 Corporación Universidad de la Costa REDICUC - Repositorio CUC |
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https://hdl.handle.net/11323/14123 https://repositorio.cuc.edu.co/ |
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eng |
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eng |
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AIMS Mathematics |
| dc.relation.references.none.fl_str_mv |
G. Dattotli, S. Lorenzutta, C. Cesarano, Bernstein polynomials and operational methods, J. Comput. Anal. Appl., 8 (2006), 369–377. G. Dattoli, Hermite-Bessel and Laguerre-Bessel functions: a by-product of the monomiality principle, In: D. Cocolicchio, G. Dattoli, H. M. Srivastava, Advanced special functions and applications, Melfi, May 9–12, 1999, Rome: Aracne Editrice, 2000, 147–164. T. Nahid, J. Choi, Certain hybrid matrix polynomials related to the Laguerre-Sheffer family, Fractal Fract., 6 (2022), 211. https://doi.org/10.3390/fractalfract6040211 S. A. Wani, K. Abuasbeh, G. I. Oros, S. Trabelsi, Studies on special polynomials involving degenerate Appell polynomials and fractional derivative, Symmetry, 15 (2023), 840. https://doi.org/10.3390/sym15040840 R. Alyusof, S. A. Wani, Certain properties and applications of ∆h hybrid special polynomials associated with Appell sequences, Fractal Fract., 7 (2023), 233. https://doi.org/10.3390/fractalfract7030233 H. M. Srivastava, G. Yasmin, A. Muhyi, S. Araci, Certain results for the twice-iterated 2D q-Appell polynomials, Symmetry, 11 (2019), 1307. https://doi.org/10.3390/sym11101307 A. M. Obad, A. Khan, K. S. Nisar, A. Morsy, q-binomial convolution and transformations of q-Appell polynomials, Axioms, 10 (2021), 70. https://doi.org/10.3390/axioms10020070 D. Bedoya, O. Ortega, W. Ram´ırez, U. Urieles, New biparametric families of Apostol-FrobeniusEuler polynomials of level m, Mat. Stud., 55 (2021), 10–23. https://doi.org/10.30970/ms.55.1.10- 23 N. Kılar, Y. Simsek, Combinatorial sums involving Fubini type numbers and other special numbers and polynomials: approach trigonometric functions and p-adic integrals, Adv. Stud. Contemp. Math., 31 (2021), 75–87 N. Kılar, Y. Simsek, Identities and relations for Hermite-based Milne-Thomson polynomials associated with Fibonacci and Chebyshev polynomials, RACSAM, 115 (2021), 28. https://doi.org/10.1007/s13398-020-00968-3 N. Kılar, Y. Simsek, A note on Hermite-based Milne Thomson type polynomials involving Chebyshev polynomials and other polynomials, Sci. J. Mehmet Akif Ersoy Univ., 3 (2020), 8–14 Y. Simsek, Formulas for Poisson-Charlier, Hermite, Milne-Thomson and other type polynomials by their generating functions and p-adic integral approach, RACSAM, 113 (2019), 931–948. https://doi.org/10.1007/s13398-018-0528-6 Y. Simsek, N. Cakic, Identities associated with Milne-Thomson type polynomials and special numbers, J. Inequal. Appl., 2018 (2018), 84. https://doi.org/10.1186/s13660-018-1679-x R. Dere, Y. Simsek, Hermite base Bernoulli type polynomials on the umbral algebra, Russ. J. Math. Phys., 22 (2015), 1–5. https://doi.org/10.1134/S106192081501001X G. Dattoli, Generalized polynomials operational identities and their applications, J. Comput. Appl. Math., 118 (2000), 111–123. https://doi.org/10.1016/S0377-0427(00)00283-1 P. Appell, J. K. de Feriet, ´ Fonctions hypergeom ´ etriques et hypersph ´ eriques: polyn ´ omes d’Hermite ˆ , Paris: Gauthier-Villars, 1926 L. C. Andrews, Special functions for engineers and applied mathematicians, New York: Macmillan Publishing Company, 1985 G. Dattoli, Summation formulae of special functions and multivariable Hermite polynomials, Nuovo Cimento-B, 119B (2004), 479–488. https://doi.org/10.1393/ncb/i2004-10111-1 M. A. Ozarslan, Unified Apostol-Bernoulli, Euler and Genocchi polynomials, ¨ Comput. Math. Appl., 62 (2011), 2452–2462. https://doi.org/10.1016/j.camwa.2011.07.031 Q. M. Luo, Apostol-Euler polynomials of higher order and the Gaussian hypergeometric function, Taiwanese J. Math., 10 (2006), 917–925. https://doi.org/10.11650/twjm/1500403883 A. Erdelyi, ´ Higher transcendental functions, McGraw-Hill Book Company, 1955 L. Carlitz, Eulerian numbers and polynomials, Math. Mag., 32 (1959), 247–260. https://doi.org/10.2307/3029225 K. B. Oldham, J. Spanier, The fractional calculas, Theory and Applications of Differentiation and Integration to Arbitrary Order, Academic Press, 1974 D. V. Widder, An introduction to transform theory, New York: Academic Press, 1971 G. Dattoli, P. E. Ricci, C. Cesarano, L. Vazquez, Special polynomials and fractional calculus, ´ Math. Comput. Modell., 37 (2003), 729–733. https://doi.org/10.1016/S0895-7177(03)00080-3 D. Assante, C. Cesarano, C. Fornaro, L. Vazquez, Higher order and fractional diffusive equations, J. Eng. Sci. Technol. Rev., 8 (2015), 202–204. https://doi.org/10.25103/JESTR.085.25 J. F. Steffensen, The poweriod, an extension of the mathematical notion of power, Acta. Math., 73 (1941), 333–366 B. Kurt, Y. Simsek, Frobenius-Euler type polynomials related to Hermite-Bernoulli polyomials, AIP Conf. Proc., 1389 (2011), 385–388. https://doi.org/10.1063/1.3636743 Y. Simsek, Generating functions for q-Apostol type Frobenius-Euler numbers and polynomials, Axioms, 1 (2012), 395–403. https://doi.org/10.3390/axioms1030395 D. S. Kim, T. Kim, Some new identities of Frobenius-Euler numbers and polynomials, J. Inequal. Appl., 307 (2012), 307. https://doi.org/10.1186/1029-242X-2012-307 |
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Atribución 4.0 Internacional (CC BY 4.0)© 2024 The Author(s)https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Zayed, MohraWani, Shahid AhmadOros, Georgia IrinaRamírez, Williamvirtual::1048-12025-04-07T20:22:58Z2025-04-07T20:22:58Z2024-05-09Mohra Zayed, Shahid Ahmad Wani, Georgia Irina Oros, William Ramŕez. A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators[J]. AIMS Mathematics, 2024, 9(6): 16297-16312. doi: 10.3934/math.20247892473-6988https://hdl.handle.net/11323/1412310.3934/math.2024789Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/riginally developed within the realm of mathematical physics, integral transformations have transcended their origins and now find wide application across various mathematical domains. Among these applications, the construction and analysis of special polynomials benefit significantly from the elucidation of generating expressions, operational principles, and other distinctive properties. This study delves into a pioneering exploration of an extended lineage of Frobenius-Euler polynomials belonging to the Hermite-Apostol type, incorporating multivariable variables through fractional operators. Motivated by the exigencies of contemporary engineering challenges, the research endeavors to uncover the operational rules and establishing connections inherent within these extended polynomials. In doing so, it seeks to chart a course towards harnessing these mathematical constructs within diverse engineering contexts, where their unique attributes hold the potential for yielding profound insights. The study deduces operational rules for this generalized family, facilitating the establishment of generating connections and the identification of recurrence relations. Furthermore, it showcases compelling applications, demonstrating how these derived polynomials may offer meaningful solutions within specific engineering scenarios.16 páginasapplication/pdfengAIMS PressUnited Stateshttps://www.aimspress.com/article/doi/10.3934/math.2024789A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operatorsArtículo de revistahttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85AIMS MathematicsG. Dattotli, S. Lorenzutta, C. Cesarano, Bernstein polynomials and operational methods, J. Comput. Anal. Appl., 8 (2006), 369–377.G. Dattoli, Hermite-Bessel and Laguerre-Bessel functions: a by-product of the monomiality principle, In: D. Cocolicchio, G. Dattoli, H. M. Srivastava, Advanced special functions and applications, Melfi, May 9–12, 1999, Rome: Aracne Editrice, 2000, 147–164.T. Nahid, J. Choi, Certain hybrid matrix polynomials related to the Laguerre-Sheffer family, Fractal Fract., 6 (2022), 211. https://doi.org/10.3390/fractalfract6040211S. A. Wani, K. Abuasbeh, G. I. Oros, S. Trabelsi, Studies on special polynomials involving degenerate Appell polynomials and fractional derivative, Symmetry, 15 (2023), 840. https://doi.org/10.3390/sym15040840R. Alyusof, S. A. Wani, Certain properties and applications of ∆h hybrid special polynomials associated with Appell sequences, Fractal Fract., 7 (2023), 233. https://doi.org/10.3390/fractalfract7030233H. M. Srivastava, G. Yasmin, A. Muhyi, S. Araci, Certain results for the twice-iterated 2D q-Appell polynomials, Symmetry, 11 (2019), 1307. https://doi.org/10.3390/sym11101307A. M. Obad, A. Khan, K. S. Nisar, A. Morsy, q-binomial convolution and transformations of q-Appell polynomials, Axioms, 10 (2021), 70. https://doi.org/10.3390/axioms10020070D. Bedoya, O. Ortega, W. Ram´ırez, U. Urieles, New biparametric families of Apostol-FrobeniusEuler polynomials of level m, Mat. Stud., 55 (2021), 10–23. https://doi.org/10.30970/ms.55.1.10- 23N. Kılar, Y. Simsek, Combinatorial sums involving Fubini type numbers and other special numbers and polynomials: approach trigonometric functions and p-adic integrals, Adv. Stud. Contemp. Math., 31 (2021), 75–87N. Kılar, Y. Simsek, Identities and relations for Hermite-based Milne-Thomson polynomials associated with Fibonacci and Chebyshev polynomials, RACSAM, 115 (2021), 28. https://doi.org/10.1007/s13398-020-00968-3N. Kılar, Y. Simsek, A note on Hermite-based Milne Thomson type polynomials involving Chebyshev polynomials and other polynomials, Sci. J. Mehmet Akif Ersoy Univ., 3 (2020), 8–14Y. Simsek, Formulas for Poisson-Charlier, Hermite, Milne-Thomson and other type polynomials by their generating functions and p-adic integral approach, RACSAM, 113 (2019), 931–948. https://doi.org/10.1007/s13398-018-0528-6Y. Simsek, N. Cakic, Identities associated with Milne-Thomson type polynomials and special numbers, J. Inequal. Appl., 2018 (2018), 84. https://doi.org/10.1186/s13660-018-1679-xR. Dere, Y. Simsek, Hermite base Bernoulli type polynomials on the umbral algebra, Russ. J. Math. Phys., 22 (2015), 1–5. https://doi.org/10.1134/S106192081501001XG. Dattoli, Generalized polynomials operational identities and their applications, J. Comput. Appl. Math., 118 (2000), 111–123. https://doi.org/10.1016/S0377-0427(00)00283-1P. Appell, J. K. de Feriet, ´ Fonctions hypergeom ´ etriques et hypersph ´ eriques: polyn ´ omes d’Hermite ˆ , Paris: Gauthier-Villars, 1926L. C. Andrews, Special functions for engineers and applied mathematicians, New York: Macmillan Publishing Company, 1985G. Dattoli, Summation formulae of special functions and multivariable Hermite polynomials, Nuovo Cimento-B, 119B (2004), 479–488. https://doi.org/10.1393/ncb/i2004-10111-1M. A. Ozarslan, Unified Apostol-Bernoulli, Euler and Genocchi polynomials, ¨ Comput. Math. Appl., 62 (2011), 2452–2462. https://doi.org/10.1016/j.camwa.2011.07.031Q. M. Luo, Apostol-Euler polynomials of higher order and the Gaussian hypergeometric function, Taiwanese J. Math., 10 (2006), 917–925. https://doi.org/10.11650/twjm/1500403883A. Erdelyi, ´ Higher transcendental functions, McGraw-Hill Book Company, 1955L. Carlitz, Eulerian numbers and polynomials, Math. Mag., 32 (1959), 247–260. https://doi.org/10.2307/3029225K. B. Oldham, J. Spanier, The fractional calculas, Theory and Applications of Differentiation and Integration to Arbitrary Order, Academic Press, 1974D. V. Widder, An introduction to transform theory, New York: Academic Press, 1971G. Dattoli, P. E. Ricci, C. Cesarano, L. Vazquez, Special polynomials and fractional calculus, ´ Math. Comput. Modell., 37 (2003), 729–733. https://doi.org/10.1016/S0895-7177(03)00080-3D. Assante, C. Cesarano, C. Fornaro, L. Vazquez, Higher order and fractional diffusive equations, J. Eng. Sci. Technol. Rev., 8 (2015), 202–204. https://doi.org/10.25103/JESTR.085.25J. F. Steffensen, The poweriod, an extension of the mathematical notion of power, Acta. Math., 73 (1941), 333–366B. Kurt, Y. Simsek, Frobenius-Euler type polynomials related to Hermite-Bernoulli polyomials, AIP Conf. Proc., 1389 (2011), 385–388. https://doi.org/10.1063/1.3636743Y. Simsek, Generating functions for q-Apostol type Frobenius-Euler numbers and polynomials, Axioms, 1 (2012), 395–403. https://doi.org/10.3390/axioms1030395D. S. Kim, T. Kim, Some new identities of Frobenius-Euler numbers and polynomials, J. Inequal. Appl., 307 (2012), 307. https://doi.org/10.1186/1029-242X-2012-307163121629769ApplicationsEulers’ integralExplicit formFractional operatorsMultivariable special polynomialsOperational connectionPublication38aeab65-0e76-44a5-8e3e-a13f48515f3dvirtual::1048-138aeab65-0e76-44a5-8e3e-a13f48515f3dvirtual::1048-10000-0003-4675-0221virtual::1048-1ORIGINALA study on extended form of multivariable Hermite-Apostol type.pdfA study on extended form of multivariable Hermite-Apostol type.pdfapplication/pdf252967https://repositorio.cuc.edu.co/bitstreams/40409b78-9782-4dd5-918f-3d18829fe264/download3f257c4ad341a50c9a718fead7487ed0MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-815543https://repositorio.cuc.edu.co/bitstreams/30ab9397-64af-4ddd-8640-ac3a9e5f22ff/download73a5432e0b76442b22b026844140d683MD52TEXTA study on extended form of multivariable Hermite-Apostol type.pdf.txtA study on extended form of multivariable Hermite-Apostol type.pdf.txtExtracted 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ara ejercer estos derechos sobre la Obra tal y como se indica a continuación:</p>
    <ol type="a">
      <li>Reproducir la Obra, incorporar la Obra en una o más Obras Colectivas, y reproducir la Obra incorporada en las Obras Colectivas.</li>
      <li>Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.</li>
      <li>Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.</li>
    </ol>
    <p>Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).</p>
  </li>
  <br/>
  <li>
    Restricciones.
    <p>La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:</p>
    <ol type="a">
      <li>Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).</li>
      <li>Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.</li>
      <li>Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.</li>
      <li>
        Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:
        <ol type="i">
          <li>Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.</li>
          <li>Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.</li>
        </ol>
      </li>
      <li>Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.</li>
    </ol>
  </li>
  <br/>
  <li>
    Representaciones, Garantías y Limitaciones de Responsabilidad.
    <p>A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.</p>
  </li>
  <br/>
  <li>
    Limitación de responsabilidad.
    <p>A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.</p>
  </li>
  <br/>
  <li>
    Término.
    <ol type="a">
      <li>Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.</li>
      <li>Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.</li>
    </ol>
  </li>
  <br/>
  <li>
    Varios.
    <ol type="a">
      <li>Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.</li>
      <li>Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.</li>
      <li>Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.</li>
      <li>Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.</li>
    </ol>
  </li>
  <br/>
</ol>
 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