IJPAM: Volume 64, No. 4 (2010)

THE WRIGHT FUNCTION AND
ITS NUMERICAL EVALUATION

Y.F. Luchko$^1$, J.J. Trujillo$^2$, M.P. Velasco$^3$
$^1$Department of Mathematics II
Technical University of Applied Sciences Berlin
10, Luxemburger Str., Berlin, 13353, GERMANY
e-mail: [email protected]
$^2$Departamento de Análisis Matemático
Universidad de La Laguna
La Laguna, 38271, SPAIN
e-mail: [email protected]
$^3$Departamento de Matemática Aplicada
Universidad Complutense de Madrid
Madrid, 28040, SPAIN
e-mail: [email protected]


Abstract.Whereas the theory of the Wright function is already well studied, its numerical evaluation is an open problem yet. Here summation of series, integral representations, and asymptotical expansions are presented. For the complex plane different numerical techniques are used and estimates for accuracy of the computations are provided. The techniques employed in the paper could be used for numerical evaluation of other functions of the hypergeometric type.

Received: November 14, 2010

AMS Subject Classification: 34A08, 33E12, 33E20, 65D20, 33F05, 30E15

Key Words and Phrases: Wright function, integral and asymptotic representations, numerical evaluation, special functions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 4