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.

中文翻译：

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经典特殊功能的多个zeta值

我们计算从各种完整函数（通常是具有物理相关性的特殊函数）的零构建的多个zeta值（MZV）。在通常情况下，MZV及其线性组合是使用对称函数和多个zeta值之间的态射来评估的。我们证明了该技术可以扩展到任何整个函数的零，并且作为说明，我们基于Bessel，Airy和Kummer超几何函数的零显式计算了一些MZV。我们重点介绍了MZV理论的几种方法，例如，利用各种多项式的正交性以及充分利用整个函数的Weierstrass表示。在此过程中，将重新讨论由Gessel和Viennot提供的Bernoulli数的恒等式，并将其推广到Bessel–Bernoulli多项式，