Jacobi transform

Summary

The Jacobi transform is a finite integral transform on $[-1, 1]$. It sends a function to the sequence of its integrals against the Jacobi polynomials $P_n^{(\alpha, \beta)}$ with their weight. It is the coefficient map of the expansion of a function in Jacobi polynomials. It turns the Jacobi differential operator into multiplication by $-n(n + \alpha + \beta + 1)$, so it is used to solve boundary value problems on an interval. The Gegenbauer and Legendre transforms are special cases.