On integrals and sums involving special functions

Integrals and sums involving special functions are in constant demand in applied mathematics. Rather than refer to a handbook of integrals or to a computer algebra system, we present a do-it-yourself systematic approach that shows how the evaluation of such integrals and sums can be made as simple as possible. Illustrating our method, we present several examples of integrals of Poisson type, Fourier transform, as well as integrals involving product of Bessel functions. We also obtain a new identity involving the sums of ₂F₁.