LAPLACE TRANSFORMS OF SOME TYPICAL EXPONENTIAL FUNCTIONS
By
M. I. Qureshi1 , Dilshad Ahamad2 and Kaleem A. Quraishi2,*
1Department of Applied Sciences and Humanities, Faculty of Engineering and Technology Jamia Millia Islamia (A Central University), New Delhi, India-110025
2Department of Applied Sciences and Humanities, Mewat Engineering College (Waqf), Nuh, Mewat, Haryana, India-122107
*Corresponding Author Email: miqureshi delhi@yahoo.co.in; dlshdhmd4@gmail.com; kaleemspn@gmail.com
(Received: March 17, 2024; In format: October 16, 2024; Revised: November 15, 2024; Accepted: November 19, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54221
Abstract
Laplace transforms of some mathematical functions constitute the basis of the present study. In this paper, using contour integration of the Mellin-Barnes type, we provide the solutions of the Laplace transforms of some typical exponential functions in terms of Meijer’s G-functions. Additionally, we obtain some known and unknown special cases (whose proofs are also not available in the existing literature on Laplace transforms) of our general integrals by applying some relations between G-functions and special functions.
2020 Mathematical Sciences Classification: 44A10; 33C60; 33B10; 33C20.
Keywords: Meijer’s G-function; Laplace-transform; Mellin-Barnes type contour integral and Generalized hypergeometric function.