A multiplication theorem for the Lerch zeta function and explicit representations of the Bernoulli and Euler polynomials
A multiplication theorem for the Lerch zeta function and explicit representations of the Bernoulli and Euler polynomials
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Lerch zeta 函数的乘法定理以及伯努利和欧拉多项式的显式表示
DOI：
10.1016/j.jmaa.2005.08.013
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发表时间：
2006
影响因子：
1.3
通讯作者：
Chung
中科院分区：
文献类型：
--
作者：
Ching;Chung
得到了Lerch Zeta函数ϕ(S，a，ξ)的一个乘法定理，并由此导出了在S=−n上求整数n⩾0时，伯努利多项式和欧拉多项式的显式表示.作为推论，给出了Bernoulli多项式和Euler多项式的一些特例的显式公式。
A multiplication theorem for the Lerch zeta function ϕ(s,a,ξ) is obtained, from which, when evaluating at s=−n for integers n⩾0, explicit representations for the Bernoulli and Euler polynomials are derived in terms of two arrays of polynomials related to the classical Stirling and Eulerian numbers. As consequences, explicit formulas for some special values of the Bernoulli and Euler polynomials are given.