Numerical calculation of the extension of k-beta function and some new extensions by using two parameter k-Mittag-Leffler function

Parik Laxmi, Shilpi Jain, Praveen Agarwal and Gradimir V. Milovanović

Applied Mathematics and Computation, 2024, vol. 479, issue C

Abstract: 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.

Keywords: k-gamma function; k-beta function; Modified moments; Gaussian quadrature rule; Orthogonal polynomial; Mellin transform (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003187

DOI: 10.1016/j.amc.2024.128857

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