A representation of Jacobi functions
Authors obtain an interesting series representation of Jacobi functions \[ P_{\lambda}^{(\alpha,\beta)}(x),\quad -\leq \alpha,\beta \leq,\quad \alpha +\beta =0,\quad and\quad \lambda \geq -. \] The continuous Jacobi transform and its inverse are used to obtain the result. When \(\lambda\) is a positive integer, the series representation reduces to a single term, that is, the Jacobi polynomial of degree n. The special case corresponding to \(\alpha =\beta =0\) is also examined. This paper represents an original contribution to the subject.
scientific article; zbMATH DE number 3951000