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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References
Ali, M.: Operational rules and generalized special polynomials. Forum Mathematicum 32(2), 269–277 (2020)
Ali, M., Nahid, T., Khan, S.: Some results on hybrid relatives of the Sheffer polynomials via operational rules. Miskolc Math. Notes 20(2), 729–743 (2019)
Andrews, L.C.: Special functions for engineers and applied mathematicians. Macmillan Publishing Company, New York (1985)
Dattoli, G.: Hermite-Bessel and Laguerre-Bessel functions: a by-product of the monomiality principle, Advanced Special Functions and Applications (Melfi, 1999), 147–164, Proc. Melfi Sch. Adv. Top. Math. Phys. 1, Aracne, Rome (2000)
Dattoli, G., Gainnnessi, L., Mezi, L., Torre, A.: Theory of generalized Bessel functions. Nuovo Cimento. 105(3), 327–347 (1990)
Dattoli, G., Ottaviani, P.. L., Torre, A., Vázquez, L.: Evolution operator equations: integration with algebraic and finite-difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory. Riv. Nuovo Cimento Soc. Ital. Fis 20(2), 1–133 (1997)
Dattoli, G., Ricci, P.E., Cesarano, C., Vázquez, L.: Special polynomials and fractional calculas. Math. Comput. Model. 37, 729–733 (2003)
Khan, S., Ali Al-Gonah, A.: Operational methods and Laguerre-Gould Hopper polynomials. Appl. Math. Comput 218, 9930–9942 (2012)
Khan, S., Ali, M., Naikoo, S.A.: Finding discrete Bessel and Tricomi convolutions of certain special polynomials. Rep. Math. Phys. 81(3), 385–397 (2018)
Khan, S., Raza, N., Ali, M.: Finding mixed families of special polynomials associated with Appell sequences. J. Math. Anal. Appl. 447, 398–418 (2017)
Rainville, E.D.: Special Functions, Reprint of 1960, 1st edn. Chelsea Publishig Co., Bronx, New York (1971)
Srivastava, H.M., Daoust, M.C.: Certain generalized Neumann expansions associated with the Kampé de Fériet function. Nederl. Akad. Wetensch. Proc. Ser. A 72 = Indag. Math. 31, 449–457 (1969)
Srivastava, H.M., Manocha, H.L.: A Treatise on Generating Functions. Halsted Press, New York (1984)
Steffensen, J.F.: The poweroid, an extension of the mathematical notion of power. Acta. Math. 73, 333–366 (1941)
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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Ali, M., Qureshi, M.I. A new class of mixed Bessel functions via integral transforms. Math Sci 15, 405–411 (2021). https://doi.org/10.1007/s40096-021-00385-6
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DOI: https://doi.org/10.1007/s40096-021-00385-6