Inhomogeneous Whittaker Equation with Initial and Boundary Conditions

M. S. Abu Zaytoon, Hannah Al Ali and M. H. Hamdan ()
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M. S. Abu Zaytoon: Faculty of Mathematics and Data Science, Emirates Aviation University, Dubai P.O. Box 686, United Arab Emirates
Hannah Al Ali: Faculty of Mathematics and Data Science, Emirates Aviation University, Dubai P.O. Box 686, United Arab Emirates
M. H. Hamdan: Department of Mathematics and Statistics, University of New Brunswick, Saint John, NB E2L 4L5, Canada

Mathematics, 2025, vol. 13, issue 17, 1-17

Abstract: In this study, a semi-analytical solution to the inhomogeneous Whittaker equation is developed for both initial and boundary value problems. A new class of special integral functions Zi κ , μ f ( x ) , along with their derivatives, is introduced to facilitate the construction of the solution. The analytical properties of Zi κ , μ f ( x ) are rigorously investigated, and explicit closed-form expressions for Zi κ , μ f ( x ) and its derivatives are derived in terms of Whittaker functions M κ , μ ( z ) and W κ , μ ( z ) , confluent hypergeometric functions, and other special functions including Bessel functions, modified Bessel functions, and the incomplete gamma functions, along with their respective derivatives. These expressions are obtained for specific parameter values using symbolic computation in Maple. The results contribute to the broader analytical framework for solving inhomogeneous linear differential equations with applications in engineering, mathematical physics, and biological modeling.

Keywords: inhomogeneous Whittaker equations; Whittaker functions; integral Whittaker functions; Bessel functions; incomplete gamma functions; confluent hypergeometric function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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