In 2021, Fassari et al. introduced a remarkable summation involving the even-indexed eigenfunctions of the quantum harmonic oscillator, and introduced a proof, based on manipulations of multiple elliptic integrals, for an evaluation involving Catalan's constant for the aforementioned summation. This motivates the development of generalizations and extensions of this evaluation. In this article, we show, using the Wilf–Zeilberger method, how this series evaluation may be extended to infinite families of hypergeometric expressions that have free parameters and that are explicitly evaluable in terms of the digamma function. We also consider how an identity related to a nonterminating q-Pfaff–Saalschütz sum due to Krattenthaler and Srivastava may be applied to further generalize the main result due to Fassari et al.

2021 年，Fassari 等人。引入了涉及量子谐振子的偶指数本征函数的显着求和，并引入了基于多重椭圆积分操作的证明，用于涉及上述求和的 Catalan 常数的评估。这促进了该评估的概括和扩展的发展。在本文中，我们使用 Wilf-Zeilberger 方法展示了如何将级数求值扩展到具有自由参数并且可以根据 digamma 函数显式求值的无限族超几何表达式。我们还考虑如何应用与 Krattenthaler 和 Srivastava 提出的非终止q -Pfaff-Saalschütz 和相关的恒等式来进一步概括 Fassari 等人提出的主要结果。