Abstract
In this article, we get certain integral representations of the multi-index Wright generalized Bessel function by making use of the extended beta function. This function is presented as a part of the generalized Bessel–Maitland function obtained by taking the extended fractional derivative of the generalized Bessel–Maitland function developed by Özarsalan and Özergin [M. Ali Özarslan and E. Özergin, Some generating relations for extended hypergeometric functions via generalized fractional derivative operator, Math. Comput. Model. 52 2010, 9–10, 1825–1833]. In addition, we demonstrate the exciting connections of the multi-index Wright generalized Bessel function with Laguerre polynomials and Whittaker function. Further, we use the generalized Wright hypergeometric function to calculate the Mellin transform and the inverse of the Mellin transform.
References
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A family of Apostol–Euler polynomials associated with Bell polynomials
- Some finite integrals involving Mittag-Leffler confluent hypergeometric function
- Results concerning multi-index Wright generalized Bessel function
- On some new inequalities of Hermite–Hadamard–Mercer midpoint and trapezoidal type in q-calculus
- The (p,q)-sine and (p,q)-cosine polynomials and their associated (p,q)-polynomials
Artikel in diesem Heft
- Frontmatter
- A family of Apostol–Euler polynomials associated with Bell polynomials
- Some finite integrals involving Mittag-Leffler confluent hypergeometric function
- Results concerning multi-index Wright generalized Bessel function
- On some new inequalities of Hermite–Hadamard–Mercer midpoint and trapezoidal type in q-calculus
- The (p,q)-sine and (p,q)-cosine polynomials and their associated (p,q)-polynomials