ABSTRACT Discrete analogues of the classical Mehler–Fock transforms are introduced and investigated. It involves series with the associated Legendre function , x>1, , , is the imaginary unit, and the so-called incomplete Legendre integrals. Several expansions of arbitrary functions and sequences in terms of these series and integrals are established.

中文翻译：

---

离散 Mehler–Fock 变换

摘要介绍并研究了经典 Mehler-Fock 变换的离散类似物。它涉及与相关的勒让德函数的级数，x>1，……，是虚数单位，以及所谓的不完全勒让德积分。建立了关于这些级数和积分的任意函数和序列的几种展开式。