Laplace Transforms of Some Special Functions of Mathematical Physics Using Mellin-Barnes Type Contour Integration

Transcription

1 International Journal of Mathematics and Statistics Invention (IJMSI) E-ISSN: P-ISSN: Volume 3 Issue 7 November PP Laplace Transforms of Some Special Functions of Mathematical Physics Using Mellin-Barnes Type Contour Integration 1 M.I.Qureshi, 2 Deepak Kumar Kabra, 3 M. S. Baboo 1 Department of Applied Sciences and Humanities Faculty of Engineering and Technology Jamia Millia Islamia (A Central University) New Delhi , India 2 Department of Mathematics Govt. College Kota University of Kota Kota, Rajasthan , India 3 Department of Applied Sciences and Humanities Knowledge park III Sharda University Gr. Noida, U.P , India Abstract: In this paper, we find some results on Laplace transforms of Special functions like products of Ordinary Bessel s function of I kind and Modified Bessel s function of I kind, five Complete Elliptic integrals, Hyper-Bessel function of Humbert, Modified Hyper-Bessel function of Delerue, Error function, Incomplete Beta function, Incomplete Gamma function, Fresnel Integrals, Sine Integral, Hyperbolic Sine Integral, Polylogarithm function, Struve function, Modified Struve function, Lommel function, Kelvin s functions and Lerch s Transcendent, in terms of Meijer s G-function of one variable and generalized hypergeometric function of one variable, using Mellin-Barnes type contour integral technique. The results presented here are presumably new. Keywords and Phrases: Generalized Hypergeometric function, Laplace transforms, Meijer s G - function, Gauss s multiplication formula, Legendre s duplication formula and triplication formula MSC(AMS) Primary:44A10; Secondary: 33C20, 33C60. I. Introduction and Preliminaries 21 Page

2 22 Page

3 23 Page

4 II. Laplace transform 24 Page

5 III. Theorem on Laplace Transforms 25 Page

6 IV. Laplace Transforms of Special Functions of Mathematical Physics 26 Page

7 27 Page

8 28 Page

9 29 Page

10 30 Page

11 31 Page

12 32 Page

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