Finite Series of Distributional Solutions for Certain Linear Differential Equations - Nipon Waiyaworn; Kamsing Nonlaopon; Somsak Orankitjaroen (Axioms, 2020)
In this paper, we present the distributional solutions of the modified spherical Bessel differential equations <semantics>t2y″(t)+2ty′(t)−[t2+ν(ν+1)]y(t)=0</semantics> and the linear differential equations of the forms <semantics>t2y″(t)+3ty′(t)−(t2+ν2−1)y(t)=0,</semantics> where <semantics>ν∈N∪{0}</semantics> and <semantics>t∈R</semantics>. We find that the distributional solutions, in the form of a finite series of the Dirac delta function and its derivatives, depend on the values of <semantics>ν</semantics>. The results of several examples are also presented.