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On a Unification of Generalized Mittag-Leffler Function and Family of Bessel Functions
Department of Mathematical Sciences, Faculty of Applied Sciences, Charotar University of Science and Technology, Changa, India
Department of Mathematics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara, India
Department of Mathematics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara, India
- 1 Department of Mathematical Sciences, Faculty of Applied Sciences, Charotar University of Science and Technology, Changa, India
- 2 Department of Mathematics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara, India
- 3 Department of Mathematics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara, India
Advances in Pure Mathematics·Volume 03 (2013)·Pages 127–137·Published 11 January 2013·DOI10.4236/apm.2013.31017
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Abstract
In the present work, a unification of certain functions of mathematical physics is proposed and its properties are studied. The proposed function unifies Lommel function, Struve function, the Bessel-Maitland function and its generalization, Dotsenko function, generalized Mittag-Leffler function etc. The properties include absolute and uniform convergence, differential recurrence relation, integral representations in the form of Euler-Beta transform, Mellin-Barnes transform, Laplace transform and Whittaker transform. The special cases namely the generalized hypergeometric function, generalized Laguerre polynomial, Fox H-function etc. are also obtained.
KeywordsGeneralized Mittag-Leffler FunctionRecurrence RelationWiman’s Function
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