Abstract
Two generalized integrals of the beta family are the prime focus of this paper. By taking into account the generalized integral of the beta family, the series and integral representations are created through generalized special functions. Also covered are the fractional maps of Saigo, Riemann–Liouville, and Kober operators with the extended beta function. Results for classical beta function and extended beta functions were proved as special cases.
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Acknowledgements
The first author would like to thank the University of Kerala for providing partial financial support under Project No. 1622/2021/UOK to complete this research work. The authors would like to acknowledge the unknown referees for their valuable comments and suggestions, which enhanced the paper to its present form.
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The first author received partial financial support from the University of Kerala under Project No. 1622/2021/UOK.
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Kumar, D., Pathan, M.A. On a Class of Integrals of Beta Family: Series Representations and Fractional Maps. Mediterr. J. Math. 21, 95 (2024). https://doi.org/10.1007/s00009-024-02639-8
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DOI: https://doi.org/10.1007/s00009-024-02639-8
Keywords
- Beta function
- Fractional derivatives and Integrals
- Hermite polynomials
- Generalized hypergeometric series