Paper
A few identities and integrals involving Pochhammer symbols, Jacobi polynomials, and the hypergeometric function
Authors
Paweł J. Szabłowski
Abstract
We expand a hypergeometric function in an orthogonal series of Jacobi polynomials. We first identify identities involving the Pochhammer symbol (rising factorial). We utilize them to discover closed forms for certain integrals of Jacobi polynomials that are multiplied by a hypergeometric function and a Beta density. We can also obtain closed forms for particular series that consist of rising factorials, which generalize binomial series, by using well-known properties of the hypergeometric function. We can also get some simplifying identities of generalized hypergeometric functions.