New Classes of Degenerate Unified Polynomials
In this paper, we introduce a class of new classes of degenerate unified polynomials and we show some algebraic and differential properties. This class includes the Appell-type classical polynomials and their most relevant generalizations. Most of the results are proved by using generating function...
- Autores:
-
BEDOYA VALENCIA, DANIEL ALEJANDRO
Cesarano, Clemente
Díaz, Stiven
Ramirez, William
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2022
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/10378
- Acceso en línea:
- https://hdl.handle.net/11323/10378
https://repositorio.cuc.edu.co/
- Palabra clave:
- Bernoulli polynomials
Euler polynomials
Genocchi polynomials
Apostol-type polynomials
Degenerate polynomials
- Rights
- openAccess
- License
- Atribución 4.0 Internacional (CC BY 4.0)
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New Classes of Degenerate Unified Polynomials |
| title |
New Classes of Degenerate Unified Polynomials |
| spellingShingle |
New Classes of Degenerate Unified Polynomials Bernoulli polynomials Euler polynomials Genocchi polynomials Apostol-type polynomials Degenerate polynomials |
| title_short |
New Classes of Degenerate Unified Polynomials |
| title_full |
New Classes of Degenerate Unified Polynomials |
| title_fullStr |
New Classes of Degenerate Unified Polynomials |
| title_full_unstemmed |
New Classes of Degenerate Unified Polynomials |
| title_sort |
New Classes of Degenerate Unified Polynomials |
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BEDOYA VALENCIA, DANIEL ALEJANDRO Cesarano, Clemente Díaz, Stiven Ramirez, William |
| dc.contributor.author.none.fl_str_mv |
BEDOYA VALENCIA, DANIEL ALEJANDRO Cesarano, Clemente Díaz, Stiven Ramirez, William |
| dc.subject.proposal.eng.fl_str_mv |
Bernoulli polynomials Euler polynomials Genocchi polynomials Apostol-type polynomials Degenerate polynomials |
| topic |
Bernoulli polynomials Euler polynomials Genocchi polynomials Apostol-type polynomials Degenerate polynomials |
| description |
In this paper, we introduce a class of new classes of degenerate unified polynomials and we show some algebraic and differential properties. This class includes the Appell-type classical polynomials and their most relevant generalizations. Most of the results are proved by using generating function methods and we illustrate our results with some examples. |
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Bedoya, D.; Clemente, C.; Díaz, S.; Ramírez, W. New Classes of Degenerate Unified Polynomials. Axioms 2023, 12, 21. https://doi.org/ 10.3390/axioms12010021 |
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10.3390/axioms12010021 |
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2075-1680 |
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Corporación Universidad de la Costa |
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Bedoya, D.; Clemente, C.; Díaz, S.; Ramírez, W. New Classes of Degenerate Unified Polynomials. Axioms 2023, 12, 21. https://doi.org/ 10.3390/axioms12010021 10.3390/axioms12010021 2075-1680 Corporación Universidad de la Costa REDICUC - Repositorio CUC |
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eng |
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eng |
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Axioms |
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1. Abramowitz, M.; Stegun, I. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables; US Government Printing Office: Washington, DC, USA, 1964; Volume 55. 2. Apostol, T.M. Introduction to Analytic Number Theory; Springer Science & Business Media: Berlin, Germany, 1998. 3. Graham, R.L.; Knuth, D.E.; Patashnik, O.; Liu, S. Concrete mathematics: A foundation for computer science. Comput. Phys. 1989, 3, 106–107. [CrossRef] 4. Hernández-Llanos, P.; Quintana, Y.; Urieles, A. About Extensions Of Generalized Apostol-type polynomials. Results Math. 2015, 68, 203–225. [CrossRef] 5. Kurt, B. A further generalization of the Bernoulli polynomials and on the 2D–Bernoulli polynomials B 2 n (x, y). Appl. Math. Sci. 2010, 47, 2315–2322. 6. Ramírez, W.; Cesarano, C.; Díaz, S. New results for degenerated generalized Apostol-Bernoulli, Apostol-Euler and ApostolGenocchi polynomials. WSEAS Trans. Math. 2022, 21, 604–608. [CrossRef] 7. Ramírez, W.; Castilla, L.; Urieles, A. An extended generalized-extensions for the Apostol Type polynomial. Abstr. Appl. Anal. 2018, 2018, 2937950. 8. Guo-Dong, L.; Srivastava, H.M. Explicit formulas for the Norlund polynomials Bn(x) and bn(x). Comput. Math. Appl. 2006, 51, 1377–1384. 9. Horadam, A.F. Negative order Genocchi polynomials. Fibonacci Quart. 1992, 30, 21–34. 10. Apostol, T.M. On the Lerch zeta function. Pac. J. Math. 1951, 1, 161–167. [CrossRef] 11. Luo, Q.-M.; Srivastava, H.M. Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials. J. Math. Anal. Appl. 2005, 308, 290–302. [CrossRef] 12. Luo, Q.-M. Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions. Taiwan. J. Math. 2006, 10, 917–925. [CrossRef] 13. Srivastava, H.M. Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials. Appl. Math. Inf. Sci. 2011, 5, 390–444. 14. Belbachir, H.; Djemmada, Y.; Hadj-Brahim, S. Unified Bernoulli-Euler polynomials of Apostol type. Indian J. Pure Appl. Math. 2022, 1–8. [CrossRef] 15. Bedoya, D.; Ortega, M.; Ramírez, W.; Urieles, A. New results parametric Apostol-type Frobenius-Euler polynomials and their matrix approach. Kragujev. J. Math. 2025, 49, 411–429. 16. Araci, S.; Acikgoz, M. Construction of fourier expansion of Apostol Frobenius-Euler polynomials and its applications. Adv. Differ. Equ. 2018, 2018, 1–14. [CrossRef] 17. Andrews, L.C. Special Functions of Mathematics for Engineers; SPIE Press: Bellingham, WA, USA, 1998; Volume 49. 18. Cesarano, C.; Ramírez, W.; Khan, S. A new class of degenerate Apostol–type Hermite polynomials and applications. Dolomites Res. Notes Approx. 2022, 15, 1–10. 19. Hwang, K.W.; Ryoo, C.S. Some identities involving two-variable partially degenerate Hermite polynomials induced from differential equations and structure of their roots. Mathematics 2020, 8, 632. [CrossRef] 20. Khan, S.; Nahid, T.; Riyasat, M. On degenerate Apostol-type polynomials and applications. Bol. Soc. Matemática Mex. 2019, 25, 509–528. [CrossRef] 21. Carlitz, L. A degenerate Staudt–Clausen theorem. Arch. Math. 1956, 7, 28–33. [CrossRef] 22. Kim, T.; Kim, D.S. Identities involving degenerate Euler numbers and polynomials arising from nonlinear differential equations. J. Nonlinear Sci. Appl. 2016, 9, 2086–2098. [CrossRef] 23. Lim, D. Some identities of degenerate Genocchi polynomials. Bull. Korean Math. Soc. 2016, 53, 569–579. [CrossRef] 24. Gradshteyn, I.S.; Ryzhik, I.M. Table of Integrals, Series, and Products, 7th ed. Academic Press, Inc.: San Diego, CA, USA, 2007. 25. Bloch, E.D. The Real Numbers and Real Analysis; Springer: New York, NY, USA; Dordrecht, The Netherlands; Heidelberg, Geremnay; London, UK, 2011. 26. Aigner, M. Diskrete Mathematik, 6th ed.; Friedr. Vieweg & Sohn: Berlin, Germany, 2006. 27. Kim, T. A note on degenerate Stirling polynomials of the second kind. Proc. Jangjeon Math. Soc. 2017, 20, 319–331. |
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Atribución 4.0 Internacional (CC BY 4.0)© 2022 by the authors. Licensee MDPI, Basel, Switzerland.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2BEDOYA VALENCIA, DANIEL ALEJANDROCesarano, ClementeDíaz, StivenRamirez, William2023-08-10T21:58:41Z2023-08-10T21:58:41Z2022-12-25Bedoya, D.; Clemente, C.; Díaz, S.; Ramírez, W. New Classes of Degenerate Unified Polynomials. Axioms 2023, 12, 21. https://doi.org/ 10.3390/axioms12010021https://hdl.handle.net/11323/1037810.3390/axioms120100212075-1680Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/In this paper, we introduce a class of new classes of degenerate unified polynomials and we show some algebraic and differential properties. This class includes the Appell-type classical polynomials and their most relevant generalizations. Most of the results are proved by using generating function methods and we illustrate our results with some examples.10 páginasapplication/pdfengSwitzerlandSwitzerlandhttps://www.mdpi.com/2075-1680/12/1/21New Classes of Degenerate Unified PolynomialsArtículo 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_970fb48d4fbd8a85Axioms1. Abramowitz, M.; Stegun, I. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables; US Government Printing Office: Washington, DC, USA, 1964; Volume 55.2. Apostol, T.M. Introduction to Analytic Number Theory; Springer Science & Business Media: Berlin, Germany, 1998.3. Graham, R.L.; Knuth, D.E.; Patashnik, O.; Liu, S. Concrete mathematics: A foundation for computer science. Comput. Phys. 1989, 3, 106–107. [CrossRef]4. Hernández-Llanos, P.; Quintana, Y.; Urieles, A. About Extensions Of Generalized Apostol-type polynomials. Results Math. 2015, 68, 203–225. [CrossRef]5. Kurt, B. A further generalization of the Bernoulli polynomials and on the 2D–Bernoulli polynomials B 2 n (x, y). Appl. Math. Sci. 2010, 47, 2315–2322.6. Ramírez, W.; Cesarano, C.; Díaz, S. New results for degenerated generalized Apostol-Bernoulli, Apostol-Euler and ApostolGenocchi polynomials. WSEAS Trans. Math. 2022, 21, 604–608. [CrossRef]7. Ramírez, W.; Castilla, L.; Urieles, A. An extended generalized-extensions for the Apostol Type polynomial. Abstr. Appl. Anal. 2018, 2018, 2937950.8. Guo-Dong, L.; Srivastava, H.M. Explicit formulas for the Norlund polynomials Bn(x) and bn(x). Comput. Math. Appl. 2006, 51, 1377–1384.9. Horadam, A.F. Negative order Genocchi polynomials. Fibonacci Quart. 1992, 30, 21–34.10. Apostol, T.M. On the Lerch zeta function. Pac. J. Math. 1951, 1, 161–167. [CrossRef]11. Luo, Q.-M.; Srivastava, H.M. Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials. J. Math. Anal. Appl. 2005, 308, 290–302. [CrossRef]12. Luo, Q.-M. Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions. Taiwan. J. Math. 2006, 10, 917–925. [CrossRef]13. Srivastava, H.M. Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials. Appl. Math. Inf. Sci. 2011, 5, 390–444.14. Belbachir, H.; Djemmada, Y.; Hadj-Brahim, S. Unified Bernoulli-Euler polynomials of Apostol type. Indian J. Pure Appl. Math. 2022, 1–8. [CrossRef]15. Bedoya, D.; Ortega, M.; Ramírez, W.; Urieles, A. New results parametric Apostol-type Frobenius-Euler polynomials and their matrix approach. Kragujev. J. Math. 2025, 49, 411–429.16. Araci, S.; Acikgoz, M. Construction of fourier expansion of Apostol Frobenius-Euler polynomials and its applications. Adv. Differ. Equ. 2018, 2018, 1–14. [CrossRef]17. Andrews, L.C. Special Functions of Mathematics for Engineers; SPIE Press: Bellingham, WA, USA, 1998; Volume 49.18. Cesarano, C.; Ramírez, W.; Khan, S. A new class of degenerate Apostol–type Hermite polynomials and applications. Dolomites Res. Notes Approx. 2022, 15, 1–10.19. Hwang, K.W.; Ryoo, C.S. Some identities involving two-variable partially degenerate Hermite polynomials induced from differential equations and structure of their roots. Mathematics 2020, 8, 632. [CrossRef]20. Khan, S.; Nahid, T.; Riyasat, M. On degenerate Apostol-type polynomials and applications. Bol. Soc. Matemática Mex. 2019, 25, 509–528. [CrossRef]21. Carlitz, L. A degenerate Staudt–Clausen theorem. Arch. Math. 1956, 7, 28–33. [CrossRef]22. Kim, T.; Kim, D.S. Identities involving degenerate Euler numbers and polynomials arising from nonlinear differential equations. J. Nonlinear Sci. Appl. 2016, 9, 2086–2098. [CrossRef]23. Lim, D. Some identities of degenerate Genocchi polynomials. Bull. Korean Math. Soc. 2016, 53, 569–579. [CrossRef]24. Gradshteyn, I.S.; Ryzhik, I.M. Table of Integrals, Series, and Products, 7th ed. Academic Press, Inc.: San Diego, CA, USA, 2007.25. Bloch, E.D. The Real Numbers and Real Analysis; Springer: New York, NY, USA; Dordrecht, The Netherlands; Heidelberg, Geremnay; London, UK, 2011.26. Aigner, M. Diskrete Mathematik, 6th ed.; Friedr. Vieweg & Sohn: Berlin, Germany, 2006.27. Kim, T. A note on degenerate Stirling polynomials of the second kind. Proc. Jangjeon Math. Soc. 2017, 20, 319–331.101112Bernoulli polynomialsEuler polynomialsGenocchi polynomialsApostol-type polynomialsDegenerate polynomialsPublicationORIGINALNew Classes of Degenerate Unified Polynomials.pdfNew Classes of Degenerate Unified Polynomials.pdfArtículoapplication/pdf377554https://repositorio.cuc.edu.co/bitstreams/3dd38f3d-7ef2-44c8-9139-4d98aef49180/download9e567a5b4a874847d14ac28d156792f3MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-814828https://repositorio.cuc.edu.co/bitstreams/eb457f99-e858-46d7-9418-3bc01cf85cef/download2f9959eaf5b71fae44bbf9ec84150c7aMD52TEXTNew Classes of Degenerate Unified Polynomials.pdf.txtNew Classes of Degenerate Unified Polynomials.pdf.txtExtracted texttext/plain22128https://repositorio.cuc.edu.co/bitstreams/2a99b2ac-a1bc-4c62-b15c-aaa4a42efa2d/downloadf6c0280314a423c91144fd12180a5790MD53THUMBNAILNew Classes of Degenerate Unified Polynomials.pdf.jpgNew Classes of Degenerate Unified Polynomials.pdf.jpgGenerated Thumbnailimage/jpeg13511https://repositorio.cuc.edu.co/bitstreams/9c52bba7-22a7-42a1-8899-5d89e03d8067/download4351bb7e685730a3b6998d7e70b9d21bMD5411323/10378oai:repositorio.cuc.edu.co:11323/103782024-09-16 16:34:21.888https://creativecommons.org/licenses/by/4.0/© 2022 by the authors. Licensee MDPI, Basel, Switzerland.open.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa 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ada en las Obras Colectivas.

b.	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.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
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).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	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).

b.	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.

c.	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.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	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.

ii.	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.

e.	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.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
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.

6. Limitación de responsabilidad.
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.

7. Término.

a.	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.

b.	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.

8. Varios.

a.	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.

b.	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.

c.	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.

d.	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.
 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