Missouri Journal of Mathematical Sciences

On Integrals and Sums Involving Special Functions

Ahmad Al-Salman, Mohamed Ben Haj Rhouma, and Ali A. Al-Jarrah

Full-text: Open access

Abstract

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 $_{2}F_{1}$.

Article information

Source
Missouri J. Math. Sci., Volume 23, Issue 2 (2011), 123-141.

Dates
First available in Project Euclid: 11 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1321045141

Digital Object Identifier
doi:10.35834/mjms/1321045141

Mathematical Reviews number (MathSciNet)
MR2920060

Zentralblatt MATH identifier
1248.33029

Subjects
Primary: 33D15: Basic hypergeometric functions in one variable, $_r\phi_s$
Secondary: 40C15: Function-theoretic methods (including power series methods and semicontinuous methods) 34B30: Special equations (Mathieu, Hill, Bessel, etc.) 39A13: Difference equations, scaling ($q$-differences) [See also 33Dxx]

Citation

Al-Salman, Ahmad; Rhouma, Mohamed Ben Haj; Al-Jarrah, Ali A. On Integrals and Sums Involving Special Functions. Missouri J. Math. Sci. 23 (2011), no. 2, 123--141. doi:10.35834/mjms/1321045141. https://projecteuclid.org/euclid.mjms/1321045141


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