Some remarks on the generalized Apostol-Bernoulli and Apostol-Euler polynomials. (English) Zbl 1455.11038
Summary: In this paper, we give explicit expressions for generalized Apostol-Bernoulli and Apostol-Euler polynomials. As consequences, we deduce some explicit representations for other Apostol-type polynomials. Moreover, we find an algorithm based on a three-term recurrence for the calculation of generalized Apostol-Euler numbers and polynomials. As an application, we derive a formula for the values of some kinds of Hurwitz-Lerch Zeta functions at negative arguments.
MSC:
| 11B68 | Bernoulli and Euler numbers and polynomials |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
Keywords:
Apostol-Bernoulli polynomials; Apostol-Euler polynomials; Hurwitz-Lerch-zeta functions; recurrence relations; Stirling numbersReferences:
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