# Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values

• Volume: 11, Issue: 1, page 57-75
• ISSN: 1311-0454

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## Abstract

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2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15The paper deals with analysis of several techniques and methods for the numerical evaluation of the Wright function. Even if the focus is mainly on the real arguments’ values, the methods introduced here can be used in the complex plane, too. The approaches presented in the paper include integral representations of the Wright function, its asymptotic expansions and summation of series. Because the Wright function depends on two parameters and on one (in general case, complex) argument, different numerical techniques are employed for different parameters’ values. In every case, estimates for accuracy of the computations are provided. The ideas and techniques employed in the paper can be used for numerical evaluation of other functions of the hypergeometric type.

## How to cite

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Luchko, Yury. "Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values." Fractional Calculus and Applied Analysis 11.1 (2008): 57-75. <http://eudml.org/doc/11309>.

@article{Luchko2008,
abstract = {2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15The paper deals with analysis of several techniques and methods for the numerical evaluation of the Wright function. Even if the focus is mainly on the real arguments’ values, the methods introduced here can be used in the complex plane, too. The approaches presented in the paper include integral representations of the Wright function, its asymptotic expansions and summation of series. Because the Wright function depends on two parameters and on one (in general case, complex) argument, different numerical techniques are employed for different parameters’ values. In every case, estimates for accuracy of the computations are provided. The ideas and techniques employed in the paper can be used for numerical evaluation of other functions of the hypergeometric type.},
author = {Luchko, Yury},
journal = {Fractional Calculus and Applied Analysis},
keywords = {33E12; 65D20; 33F05; 30E15},
language = {eng},
number = {1},
pages = {57-75},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values},
url = {http://eudml.org/doc/11309},
volume = {11},
year = {2008},
}

TY - JOUR
AU - Luchko, Yury
TI - Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values
JO - Fractional Calculus and Applied Analysis
PY - 2008
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 11
IS - 1
SP - 57
EP - 75
AB - 2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15The paper deals with analysis of several techniques and methods for the numerical evaluation of the Wright function. Even if the focus is mainly on the real arguments’ values, the methods introduced here can be used in the complex plane, too. The approaches presented in the paper include integral representations of the Wright function, its asymptotic expansions and summation of series. Because the Wright function depends on two parameters and on one (in general case, complex) argument, different numerical techniques are employed for different parameters’ values. In every case, estimates for accuracy of the computations are provided. The ideas and techniques employed in the paper can be used for numerical evaluation of other functions of the hypergeometric type.
LA - eng
KW - 33E12; 65D20; 33F05; 30E15
UR - http://eudml.org/doc/11309
ER -

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