Geodesic
Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values
Fractional calculus and applied analysis, Tome 11 (2008) no. 1, pp. 57-75

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The 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.
Keywords: Wright Function, Special Functions, Integral Representations, Numerical Evaluation of Special Functions, Asymptotic Representations, 33E12, 65D20, 33F05, 30E15 
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Luchko, Yury. Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values. Fractional calculus and applied analysis, Tome 11 (2008) no. 1, pp. 57-75. http://geodesic.mathdoc.fr/item/FCAA_2008_11_1_a3/