Some definite integrals of Srinivasa Ramanujan and its consequences

2019/04/19 by M. I. Qureshi, Qureshi, M. I., Showkat Ahmad +1
Mathematics · #33C60 #33E20 #44A10 #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #F.2.2 #FOS: Mathematics #I.2.7 #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.1904.09070

openalex publication_date 2019/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain analytical solutions of some definite integrals of Srinivasa Ramanujan [Mess. Math., XLIV, 75-86, 1915] in terms of Meijer's G-function by using Laplace transforms of sin(βx²),cos(βx²), xsin(βx²) and xcos(βx²). Further, we obtain some infinite summation formulas connected with Meijer's G-function and numeric values of some infinite series

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