Abstract
In this chapter, we establish several integral transforms involving the product of Bessel and Whittaker functions. The results are given in terms of the Humbert and Lauricella hypergeometric functions. We also deduced some integral transforms corresponding to some particular parameters of the Whittaker function. Further, we performed some numerical simulations using the Laguerre-Gauss quadrature method, and it is proved that there is a compatibility between the numerical and theoretical predictions. Finally, as an application of our main result, we studied an intensity phenomena known as diffraction of abruptly autofocusing beam by a modulated spiral zone plate.
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Belafhal, A., Benzehoua, H., Usman, T. (2022). Evaluation of Integral Transforms in Terms of Humbert and Lauricella Functions and Their Applications. In: Singh, S., Sarigöl, M.A., Munjal, A. (eds) Algebra, Analysis, and Associated Topics. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-19082-7_13
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DOI: https://doi.org/10.1007/978-3-031-19082-7_13
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