Multiple zeta values for classical special functions

Wakhare Tanay; Vignat Christophe

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Multiple zeta values for classical special functions

机译：Multiple zeta values for classical special functions

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摘要

We compute multiple zeta values (MZVs) built from the zeros of various entire functions, usually special functions with physical relevance. In the usual case, MZVs and their linear combinations are evaluated using a morphism between symmetric functions and multiple zeta values. We show that this technique can be extended to the zeros of any entire function, and as an illustration, we explicitly compute some MZVs based on the zeros of Bessel, Airy, and Kummer hypergeometric functions. We highlight several approaches to the theory of MZVs, such as exploiting the orthogonality of various polynomials and fully utilizing the Weierstrass representation of an entire function. On the way, an identity for Bernoulli numbers by Gessel and Viennot is revisited and generalized to Bessel-Bernoulli polynomials, and the classical Euler identity between the Bernoulli numbers and Riemann zeta function at even argument is extended to this same class.

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来源
《The Ramanujan journal》 |2020年第3期|519-551|共33页
作者
Wakhare Tanay; Vignat Christophe;
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作者单位

Univ Maryland, College Pk, MD 20742 USA;

Tulane Univ, New Orleans, LA 70118 USA;

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原文格式 PDF
正文语种英语
中图分类数学;
关键词
Multiple zeta values; Bessel; Kummer hypergeometric and Airy functions; Zeros of special functions; Weierstrass factorization;

Multiple zeta values for classical special functions

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