论文标题
包含关联Legendre多项式的乘积$ p_v^u（x）p_ {ν}^{μ}（y）$：派生和评估
A Sextuple Integral Containing the Product of Associated Legendre polynomials $P_v^u(x) P_{ν}^{μ}(y)$: Derivation and Evaluation
论文作者
论文摘要
在本文中，我们得出了一个六维积分，其中包含相关的Legendre多项式的乘积$ p_v^u（x）p_ {ν}^{μ}（y）$，其中索引不同且一般。该积分的内核中包括广义对数函数和系数对数函数。该积分的推导是根据Hurwitz-Lerch Zeta函数和提高到功率的恒定系数编写的。该积分的特殊情况是根据基本常数和其他特殊功能得出的。这项工作的所有结果都是新的。
In this present paper we derive a six dimensional integral containing the product of the Associated Legendre Polynomials $P_v^u(x) P_{ν}^{μ}(y)$ where the indices are different and general. Included in the kernel of this integral is the generalized logarithmic function and coefficient logarithmic functions. The derivation of this integral is written in terms of the Hurwitz-Lerch zeta function and constant coefficients raised to a power. Special cases of this integral are derived in terms of fundamental constants and other special functions. All the results in this work are new.
