The Integral Mittag-Leffler, Whittaker and Wright Functions

Alexander Apelblat and Juan Luis González-Santander
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Alexander Apelblat: Department of Chemical Engineering, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
Juan Luis González-Santander: Department of Mathematics, Universidad de Oviedo, 33007 Oviedo, Spain

Mathematics, 2021, vol. 9, issue 24, 1-34

Abstract: Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in closed-form. In most reported cases, these new integral functions are expressed as generalized hypergeometric functions but also in terms of elementary and special functions. The behavior of some of the new integral functions is presented in graphical form. By using the MATHEMATICA program to obtain infinite sums that define the Mittag-Leffler, Whittaker, and Wright functions and also their corresponding integral functions, these functions and many new Laplace transforms of them are also reported in the Appendices for integral and fractional values of parameters.

Keywords: integral Mittag-Leffler functions; integral Whittaker functions; integral Wright functions; Laplace transforms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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