[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2020.60.4.781

Generalizations of Ramanujan's Integral Associated with Infinite Fourier Cosine Transforms in Terms of Hypergeometric Functions and its Applications

Qureshi, Mohammad Idris (Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia(A Central University))
Dar, Showkat Ahmad (Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia(A Central University))

Publication Information

Kyungpook Mathematical Journal / v.60, no.4, 2020 , pp. 781-795 More about this Journal

Abstract

In this paper, we obtain an analytical solution for an unsolved definite integral RC (m, n) from a 1915 paper of Srinivasa Ramanujan. We obtain our solution using the hypergeometric approach and an infinite series decomposition identity. Also, we give some generalizations of Ramanujan's integral RC (m, n) defined in terms of the ordinary hypergeometric function 2F3 with suitable convergence conditions. Moreover as applications of our result we obtain nine new infinite summation formulas associated with the hypergeometric functions 0F1, 1F2 and 2F3.

Keywords

generalized hypergeometric function; infinite Fourier cosine transforms; Ramanujan's integrals; Fox-Wright psi hypergeometric function; Mellin transforms; series decomposition identity; bounded sequence;

Citations & Related Records

Reference

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