Wright functions of the second kind and Whittaker functions

Abstract

In the framework of higher transcendental functions the Wright functions of the second kind have increased their relevance resulting from their applications in probability theory and, in particular, in fractional diffusion processes. Here, these functions are compared with the well-known Whittaker functions in some special cases of fractional order. In addition, we point out two erroneous representations in the literature.

16 pages, 8 figures

References in corpus (2)

• Application of the Efros theorem to the function represented by the inverse Laplace transform of $s^{-\mu }\exp (-s^{\nu })$
• On the asymptotic of Wright functions of the second kind

Cited by in corpus (3)

• Subdiffusion equation with fractional Caputo time derivative with respect to another function in modeling transition from ordinary subdiffusion to superdiffusion
• 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