Introduction and preliminaries

Abstract

We begin with a brief outline of special functions and methods, which will be needed in the next chapters. We recall here briefly the Gamma, Beta, Digamma functions, Pochhammer symbol, Bernoulli polynomials and numbers, Bessel, modified Bessel, generalized hypergeometric, Fox–Wright generalized hypergeometric, Hurwitz–Lerch Zeta functions, the Euler–Maclaurin summation formula together with Dirichlet series and Cahen’s formula, Mathieu series, Bessel and Struve differential equations, Fourier-Bessel and Dini series of Bessel functions and fractional differintegral.