Some expansion formulae for Fox's \(H\)-function of two variables involving associated Legendre functions (Q1313669)

Using the orthogonality property of associated Legendre functions and the integral formula: \[ \int^{+1}_{-1}(1-x)^{{-m\over 2}}(1+x)^ kP_ m^ k(x)dx={(-1)^{{m\over 2}}2^{k-m+1}\Gamma(k+1)\Gamma(k- m+1)\over\Gamma(k+n-m+2)\Gamma(k-n-m+1)},R(k)>m -1, \] the author first evaluates four integrals involving Fox's \(H\)-function of two variables. He then uses these results in establishing eight expansion formulas of the \(H\)-function of two variables in terms of the \(H\)-function and products of associated Legendre functions.