A new class of mixed Bessel functions via integral transforms

Abstract

Exclusive roles have been played by special functions in applied mathematics. It is not astonishing when new classes of special functions are established as the issues associated with special functions are too immense. In this article, the generalized form of hybrid Bessel functions is introduced by using suitable integral transforms and properties of exponential operators. Certain properties including generating function, series definition, operational rule and integral representation of the generalized form of hybrid Bessel functions are derived.

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Acknowledgements

This work has been sponsored by Dr. D. S. Kothari Post Doctoral Fellowship (Award letter No. F.4-2/2006(BSR)/MA/17-18/0025) awarded to Dr. Mahvish Ali by the University Grants Commission, Government of India, New Delhi.

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Correspondence to Mahvish Ali.

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Ali, M., Qureshi, M.I. A new class of mixed Bessel functions via integral transforms. Math Sci (2021). https://doi.org/10.1007/s40096-021-00385-6

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Keywords

  • Bessel functions
  • Laguerre–Gould–Hopper polynomials
  • Operational rules
  • Euler’s integral

Mathematics Subject Classification

  • 26A33
  • 65R10
  • 33B10
  • 33C45