Numerical calculation of the extension of k-beta function and some new extensions by using two parameter k-Mittag-Leffler function
A numerical method for efficient calculation of recently defined extension of k-beta functions, based on weighted quadrature formulas of Gaussian type, is proposed. The modified moments of an even exponential weight function on (−1,1), with essential singularities at ±1, are calculated in symbolic f...
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Published in | Applied mathematics and computation Vol. 479; p. 128857 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
15.10.2024
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Subjects | |
Online Access | Get full text |
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Summary: | A numerical method for efficient calculation of recently defined extension of k-beta functions, based on weighted quadrature formulas of Gaussian type, is proposed. The modified moments of an even exponential weight function on (−1,1), with essential singularities at ±1, are calculated in symbolic form in terms of the Meijer G-function. A similar problem with respect the two-parameter Mittag-Leffler function Es1,s2(z) is also considered. The Mathematica package OrthogonalPolynomials by Cvetković and Milovanović (2004) [4] is applied. Also, a new extension of k-gamma and k-beta functions by using two parameter k-Mittag-Leffler function is presented, as well as their basic properties, including some identities, a functional relation, summation and derivative formulas, integral representations and Mellin transform.
•Very efficient algorithm for numerical calculating the values of the extension of the k-beta function Bk(v1,v2;s) and the function Bs1,s2(v1,v2;s), defined by the two-parameter Mittag-Leffler function Es1,s2(z).•Methods are based on quadrature formulas of Gaussian type.•New extensions and their properties. |
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ISSN: | 0096-3003 1873-5649 |
DOI: | 10.1016/j.amc.2024.128857 |