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An Extended Generalized q‐Extensions for the Apostol Type Polynomials

Author

Listed:
  • Letelier Castilla
  • William Ramírez
  • Alejandro Urieles

Abstract

Through a modification on the parameters associated with generating function of the q‐extensions for the Apostol type polynomials of order α and level m, we obtain some new results related to a unified presentation of the q‐analog of the generalized Apostol type polynomials of order α and level m. In addition, we introduce some algebraic and differential properties for the q‐analog of the generalized Apostol type polynomials of order α and level m and the relation of these with the q‐Stirling numbers of the second kind, the generalized q‐Bernoulli polynomials of level m, the generalized q‐Apostol type Bernoulli polynomials, the generalized q‐Apostol type Euler polynomials, the generalized q‐Apostol type Genocchi polynomials of order α and level m, and the q‐Bernstein polynomials.

Suggested Citation

  • Letelier Castilla & William Ramírez & Alejandro Urieles, 2018. "An Extended Generalized q‐Extensions for the Apostol Type Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnlaaa:v:2018:y:2018:i:1:n:2937950
    DOI: 10.1155/2018/2937950
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    References listed on IDEAS

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    1. Thomas Ernst, 2012. "A Comprehensive Treatment of q-Calculus," Springer Books, Springer, edition 127, number 978-3-0348-0431-8, March.
    2. Nazim I. Mahmudov & Marzieh Eini Keleshteri, 2014. "q‐Extensions for the Apostol Type Polynomials," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Pierpaolo Natalini & Angela Bernardini, 2003. "A generalization of the Bernoulli polynomials," Journal of Applied Mathematics, Hindawi, vol. 2003, pages 1-9, January.
    4. Pierpaolo Natalini & Angela Bernardini, 2003. "A generalization of the Bernoulli polynomials," Journal of Applied Mathematics, John Wiley & Sons, vol. 2003(3), pages 155-163.
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