Generalized Generalized Mittag-Leffler function

Generalized Generalized Mittag-Leffler function in four parameters

Description

% Generalized Generalized Mittag-Leffler function
% Reference:
% [1] A.K. Shukla ?, J.C. Prajapati. "On a generalization of Mittag-Leffler
% function and its properties" J. Math. Anal. Appl. 336 (2007) 797–811
% [2] A. A. KILBAS, M. SAIGOb, and R. K. SAXENA, “Generalized
% Mittag-Leffler function and generalized fractional calculus operators,”
% Integral Transforms and Special Functions, v. 15, No. 1, 2004, pp. 31–49.
% Prepared by YangQuan Chen. 09/16/2008
% Based on the ml_fun code in Dingyu Xue, YangQuan Chen* and Derek Atherton.
% “Linear Feedback Control – Analysis and Design with Matlab”. SIAM Press, 2007,
% ISBN: 978-0-898716-38-2. (348 pages)
% Using notations in [1]
% a: \alpha \in C, and \re{\alpha) >0
% b: \beta \in C, and \re{\beta) >0
% c: \gamma \in C, and \re{\gamma) >0
% d: q \in (0,1) \union N
% x: the variable
% eps0: specified accuracy
% Definition in [1]
% E_{\alpha,\beta}^{\gamma, q} (z) =
% \sum_{n=0}^{\infty} (z^n/n!) (\gamma)_{qn} / \Gamma(\alpha n +\beta)
% see also:
% http://www.mathworks.com/
% matlabcentral/fileexchange/loadFile.do?objectId=20849&objectType=FILE
% GML_FUN is the special case of GGML_FUN when q=1
% Note: GGML_FUN converges absolutely when q< \re{\alpha) + 1

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Generalized Mittag-Leffler function

• MATLAB release: MATLAB 7.5 (R2007b)