Some results on integrals involving generalized Jacobi and related functions

Abstract

Motivated by several recent works on integrals involving various orthogonal polynomials and the natural logarithmic function, we consider a general integral I v, m a, b ( z; λ, μ), defined by equation (1.1) below, and its partial derivatives with respect to the parameters a and b. The kernel S m v ( z) of these integral formulas is a general class of functions which stem essentially from the polynomials considered, over two decades ago, by Srivastava [1]. We discuss numerous applications of our main results involving familiar special functions and polynomials. We also give a simple proof of an identity involving the Psi (or Digamma) function.