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Some Identities on the Generalized q‐Bernoulli, q‐Euler, and q‐Genocchi Polynomials

Author

Listed:
  • Daeyeoul Kim
  • Burak Kurt
  • Veli Kurt

Abstract

Mahmudov (2012, 2013) introduced and investigated some q‐extensions of the q‐Bernoulli polynomials ℬn,qαx,y of order α, the q‐Euler polynomials ℰn,qαx,y of order α, and the q‐Genocchi polynomials 𝒢n,qαx,y of order α. In this paper, we give some identities for ℬn,qαx,y, 𝒢n,qαx,y, and ℰn,qαx,y and the recurrence relations between these polynomials. This is an analogous result to the q‐extension of the Srivastava‐Pintér addition theorem in Mahmudov (2013).

Suggested Citation

  • Daeyeoul Kim & Burak Kurt & Veli Kurt, 2013. "Some Identities on the Generalized q‐Bernoulli, q‐Euler, and q‐Genocchi Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:293532
    DOI: 10.1155/2013/293532
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    References listed on IDEAS

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    1. Pierpaolo Natalini & Angela Bernardini, 2003. "A generalization of the Bernoulli polynomials," Journal of Applied Mathematics, Hindawi, vol. 2003, pages 1-9, January.
    2. Pierpaolo Natalini & Angela Bernardini, 2003. "A generalization of the Bernoulli polynomials," Journal of Applied Mathematics, John Wiley & Sons, vol. 2003(3), pages 155-163.
    3. R. Tremblay & S. Gaboury & B.-J. Fugère, 2012. "Some New Classes of Generalized Apostol-Euler and Apostol-Genocchi Polynomials," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-14, September.
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