Abstract
In this article, a family of complex Appell–Bessel functions is considered and an integral representation for this family is derived. As a consequence, cosine and sine analogs of these functions are obtained. Certain properties, including addition formulas and differential recurrence relations, are also established. Further, the degenerate complex Appell–Bessel functions are investigated, and certain results for degenerate cosine-Appell–Bessel and degenerate sine-Appell–Bessel functions are obtained. Jacobi–Anger expansions for complex Appell–Bessel functions and degenerate complex Appell–Bessel functions are explored as well.
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Acknowledgments
The authors are grateful to the referee(s) for several useful comments and suggestions towards the improvement of the paper.
Funding
This work was done under Senior Research Fellowship (File No. 09/112(0646)/2019-EMR-I dated: 13/10/2021) awarded to the second author by Council of Scientific and Industrial Research, Human resource Development Group, New Delhi.
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Khan, S., Haneef, M. & Riyasat, M. Complex Appell–Bessel Functions and Their Degenerate Analogs. Math Notes 112, 922–931 (2022). https://doi.org/10.1134/S0001434622110268
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DOI: https://doi.org/10.1134/S0001434622110268