Wright functions of the second kind and Whittaker functions

Francesco Mainardi; Richard B. Paris; Armando Consiglio

doi:10.1007/s13540-022-00042-2

Wright functions of the second kind and Whittaker functions

Francesco Mainardi^*, Richard B. Paris, Armando Consiglio

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	858-875
Number of pages	18
Journal	Fractional Calculus and Applied Analysis
Volume	25
Issue number	3
Early online date	27 May 2022
DOIs	https://doi.org/10.1007/s13540-022-00042-2
Publication status	Published - 30 Jun 2022

Keywords

Functional calculus
Wright functions
Whittaker functions
Hypergeometric functions
Laplace transform

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10.1007/s13540-022-00042-2

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author = "Francesco Mainardi and Paris, {Richard B.} and Armando Consiglio",

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AU - Paris, Richard B.

AU - Consiglio, Armando

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PY - 2022/6/30

Y1 - 2022/6/30

N2 - 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.

AB - 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.

U2 - 10.1007/s13540-022-00042-2

DO - 10.1007/s13540-022-00042-2

M3 - Article

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JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

SN - 1311-0454

IS - 3

ER -

Wright functions of the second kind and Whittaker functions

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