Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind

Waritsara Thongthai, Kamsing Nonlaopon (), Somsak Orankitjaroen and Chenkuan Li
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Waritsara Thongthai: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Kamsing Nonlaopon: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Somsak Orankitjaroen: Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
Chenkuan Li: Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada

Mathematics, 2023, vol. 11, issue 7, 1-14

Abstract: In this work, we employed the Laplace transform of right-sided distributions in conjunction with the power series method to obtain distributional solutions to the modified Bessel equation and its related equation, whose coefficients contain the parameters ν and γ . We demonstrated that the solutions can be expressed as finite linear combinations of the Dirac delta function and its derivatives, with the specific form depending on the values of ν and γ .

Keywords: Dirac delta function; distributional solution; generalized solutions; Laplace transform; power series solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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