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

Author

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

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.

Suggested Citation

  • Laxmi, Parik & Jain, Shilpi & Agarwal, Praveen & Milovanović, Gradimir V., 2024. "Numerical calculation of the extension of k-beta function and some new extensions by using two parameter k-Mittag-Leffler function," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    • Handle: RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003187
    DOI: 10.1016/j.amc.2024.128857
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