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In this present paper we derive a six dimensional integral containing theproduct of the Associated Legendre Polynomials $P_v^u(x) P_{\nu }^{\mu }(y)$where the indices are different and general. Included in the kernel of thisintegral is the generalized logarithmic function and coefficient logarithmicfunctions. The derivation of this integral is written in terms of theHurwitz-Lerch zeta function and constant coefficients raised to a power.Special cases of this integral are derived in terms of fundamental constantsand other special functions. All the results in this work are new.

A Sextuple Integral Containing the Product of Associated Legendre polynomials $P_v^u(x) P_{\nu }^{\mu }(y)$: Derivation and Evaluation