Paper Title:

On a Novel Class of Advanced Integrals of MacRobert Type Incorporating Generalized Hypergeometric Functions

Author(s):

Shwetha S Shetty and Shantha Kumari Kurumujji

Department of Mathematics, A J Institute of Engineering and Technology,
(Affiliated to Visvesvaraya Technological University (VTU), Belagavi),
Mangaluru, Karnataka,
India.
E-mail: shwethashetty576@gmail.com, shanthakk99@gmail.com

Abstract:

The main objective of this study is to evaluate two master formulas expressed as integrals over the interval from zero to π/2. These integrals involve exponential functions and trigonometric functions sine and cosine, along with ₃F₂ hypergeometric functions parameterized by general variables i and j, where i = j = 0, ± 1, ± 2, .... From these master formulas, we derive twenty-six MacRobert-type integrals by evaluating them at specific values of i and j. The results are expressed using Gamma functions. The findings given here are derived from summation formulas for the series ₄ F₃ obtained recently by Choi and Rathie along with a general result attributed to MacRobert.

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