Abstract
We introduce new extension of the extended Pochhammer symbol and gamma function by using the extended Mittag-Leffler function. We also present extension of the generalized hypergeometric function as well as some of their special cases by using this extended Pochhammer symbol. Further, we define the extension of the τ-Gauss hypergeometric function. Integral and derivative formulas involving the Mellin transform and fractional calculus techniques associated with this extended τ-Gauss hypergeometric function are also given. Also, new extended τ-Gauss hypergeometric function also provides a few more interesting and well-known results. This enriches the theory of special functions. The obtained results are believed to be newly presented.
Acknowledgements
The first author would like to express their gratitude to the University Grants Commission of India for financial assistance in the form of a Senior Research Fellowship.
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Chern flat, Chern–Ricci flat twisted product in almost Hermitian geometry
- A study of Horn matrix functions and Horn confluent matrix functions
- A common fixed point result for multi-valued mappings in Hausdorff modular fuzzy b-metric spaces with application to integral inclusions
- (L p,λ,μ,L q,λ,μ) boundedness of the G-fractional integral operator on G-Morrey spaces
- Extension of Pochhammer symbol, generalized hypergeometric function and τ-Gauss hypergeometric function
- Analysis of the beta-logarithmic function and its properties
- Regarding the set-theoretic complexity of the general fractal dimensions and measures maps
Artikel in diesem Heft
- Frontmatter
- Chern flat, Chern–Ricci flat twisted product in almost Hermitian geometry
- A study of Horn matrix functions and Horn confluent matrix functions
- A common fixed point result for multi-valued mappings in Hausdorff modular fuzzy b-metric spaces with application to integral inclusions
- (L p,λ,μ,L q,λ,μ) boundedness of the G-fractional integral operator on G-Morrey spaces
- Extension of Pochhammer symbol, generalized hypergeometric function and τ-Gauss hypergeometric function
- Analysis of the beta-logarithmic function and its properties
- Regarding the set-theoretic complexity of the general fractal dimensions and measures maps