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On integrals and sums involving special functions. (English) Zbl 1248.33029
Summary: 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 $${_2F_1}$$.
##### MSC:
 33D15 Basic hypergeometric functions in one variable, $${}_r\phi_s$$ 40C15 Function-theoretic methods (including power series methods and semicontinuous methods) for summability 34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) 39A13 Difference equations, scaling ($$q$$-differences)