On a generalized Jacobi transform (Q1394563)

The authors introduce an integral transform, which they call a generalized Jacobi transform (GJT), which can be applied to real-valued functions that are piecewise continuous on the interval \([-1,1]\). Closed form formulas are given for the GJT applied to five specific examples, and some general inequalities are also established. They also define a generalized Jacobi random variable and derive its moments, distribution function, and characteristic function.