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; Gradimir V. Milovanović

doi:10.1016/j.amc.2024.128857

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
, Gradimir V. Milovanović

Nonlinear Dynamic Research Centre (NDRC)

Poornima University
International College of Engineering
Mathematical Institute of the Serbian Academy of Sciences and Arts
University of Nis

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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 E_s₁,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.

Original language	English
Article number	128857
Journal	Applied Mathematics and Computation
Volume	479
DOIs	https://doi.org/10.1016/j.amc.2024.128857
State	Published - 15 Oct 2024

Keywords

Gaussian quadrature rule
Mellin transform
Modified moments
Orthogonal polynomial
k-beta function
k-gamma function

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10.1016/j.amc.2024.128857

Cite this

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

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 Cvetkovi{\'c} and Milovanovi{\'c} (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 = "Gaussian quadrature rule, Mellin transform, Modified moments, Orthogonal polynomial, k-beta function, k-gamma function",

author = "Parik Laxmi and Shilpi Jain and Praveen Agarwal and Milovanovi{\'c}, \{Gradimir V.\}",

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year = "2024",

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day = "15",

doi = "10.1016/j.amc.2024.128857",

language = "English",

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T1 - Numerical calculation of the extension of k-beta function and some new extensions by using two parameter k-Mittag-Leffler function

AU - Laxmi, Parik

AU - Jain, Shilpi

AU - Agarwal, Praveen

AU - Milovanović, Gradimir V.

PY - 2024/10/15

Y1 - 2024/10/15

N2 - 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.

AB - 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.

KW - Gaussian quadrature rule

KW - Mellin transform

KW - Modified moments

KW - Orthogonal polynomial

KW - k-beta function

KW - k-gamma function

UR - https://www.scopus.com/pages/publications/85194575313

U2 - 10.1016/j.amc.2024.128857

DO - 10.1016/j.amc.2024.128857

M3 - Article

AN - SCOPUS:85194575313

SN - 0096-3003

VL - 479

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 128857

ER -

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

Abstract

Keywords

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