A multiplication theorem for the Lerch zeta function and explicit representations of the Bernoulli and Euler polynomials. (English) Zbl 1102.11048
The authors derive a multiplication theorem for the Lerch zeta function \(\phi(s,a,\xi)\). They also deduce explicit representations for the Bernoulli and Euler polynomials in terms of two arrays of polynomials related to the classical Stirling and Eulerian numbers. As consequences, they give explicit formulas for some special values of the Bernoulli and Euler polynomials.
Reviewer: Hari M. Srivastava (Victoria)
MSC:
| 11M35 | Hurwitz and Lerch zeta functions |
| 11B68 | Bernoulli and Euler numbers and polynomials |
| 11B73 | Bell and Stirling numbers |
Keywords:
Lerch zeta function; Hurwitz zeta function; Eulerian polynomials; Stirling numbers; central factorial numbersReferences:
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