The integral Mittag-Leffler, Whittaker and Wright functions

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.

arXiv comment46 pages, 6 figures

References in corpus (1)

• Analytical properties and applications of the Wright function

Cited by in corpus (6)

• Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters
• Sums involving the digamma function connected to the incomplete beta function and the Bessel functions
• Finite and infinite hypergeometric sums involving the digamma function
• The Wright function -- hypergeometric representation and symbolical evaluation
• Part 2. Infinite series and logarithmic integrals associated to differentiation with respect to parameters of the Whittaker ${\mathrm{W}}_{\kappa ,\mu }\left(x\right)$ function
• Part 1. Infinite series and logarithmic integrals associated to differentiation with respect to parameters of the Whittaker ${\mathrm{M}}_{\kappa ,\mu }\left(x\right)$ function