A New Special Function with Applications to Quantum Mechanics - Chinchole, S. M. (Communications in Mathematics and Applications, 2023)
In this paper, a special function using the particular Sturm-Liouville Equation is introduced. Sequences of recurrence relations are presented for that special function. Also, its series and definite integral representations are provided. This special function is a radial solution to the Laplace equation in the 5-dimensional hyperspherical coordinate system. It is also a solution to the 4-dimensional Radial Schrödinger equation. All results are verified numerically using different mathematical softwares.