科研之友
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摘要
We show that there is a large class of Appell sequences {P-n(x)}(n=0)(infinity) for which there is a function F(s, x), entire in s for fixed x with Re x > 0 and satisfying F(-n, x) = P-n(x) for n = 0,1,2, . . . . For example, in the case of Bernoulli and Apostol-Bernoulli polynomials, F is essentially the Hurwitz zeta function and the Lerch transcendent, respectively. We study a subclass of these Appell sequences for which the corresponding special function has a form more closely related to the classical zeta functions, and give some interesting examples of these general constructions.
- 出版日期2018-3-1
