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Open AccessArticle

On a New Class of Laplace-Type Integrals Involving Generalized Hypergeometric Functions

1
Department of Mathematics, University of Kassel, Heinrich-Plett-Str. 40, D-34132 Kassel, Germany
2
Department of Mathematics Education, Wonkwang University, Iksan 570-749, Korea
3
Department of Mathematics, Vedant College of Engineering and Technology (Rajasthan Technical University), Bundi 323021, Rajasthan, India
*
Author to whom correspondence should be addressed.
Axioms 2019, 8(3), 87; https://doi.org/10.3390/axioms8030087
Received: 30 June 2019 / Revised: 17 July 2019 / Accepted: 20 July 2019 / Published: 26 July 2019
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
In the theory of generalized hypergeometric functions, classical summation theorems for the series 2 F 1 , 3 F 2 , 4 F 3 , 5 F 4 and 7 F 6 play a key role. Very recently, Masjed-Jamei and Koepf established generalizations of the above-mentioned summation theorems. Inspired by their work, the main objective of the paper is to provide a new class of Laplace-type integrals involving generalized hypergeometric functions p F p for p = 2 , 3 , 4 , 5 and 7 in the most general forms. Several new and known cases have also been obtained as special cases of our main findings. View Full-Text
Keywords: generalized hypergeometric functions; classical summation theorems; generalization; laplace transforms generalized hypergeometric functions; classical summation theorems; generalization; laplace transforms
MDPI and ACS Style

Koepf, W.; Kim, I.; Rathie, A.K. On a New Class of Laplace-Type Integrals Involving Generalized Hypergeometric Functions. Axioms 2019, 8, 87.

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