Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind - Waritsara Thongthai; Kamsing Nonlaopon; Somsak Orankitjaroen; Chenkuan Li (Mathematics, 2023)
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 <semantics>ν</semantics> and <semantics>γ</semantics>. 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 <semantics>ν</semantics> and <semantics>γ</semantics>.