A generalized formula for the integral of three associated Legendre polynomials
The authors present here a recurrence method for determining integrals \[ \int_{-1}^1 \prod_{k=1}^N P_{j_k}^{m_k} (z) dz,\qquad N=1,2,\dots, \] where the \[ P_j^m(z)= {1\over{\Gamma(1-m)}} \left( {z+1}\over{z-1}\right)^{m/2} \;_2F_1\Biggl[-j,j+1; 1-m; {{1-z}\over{2}} \Biggr] \] are associated Legendre polynomials. The application of the authors' method, with \(N=3\), for the flow over spheroids equations is also discussed.
scientific article; zbMATH DE number 1369381