Neumann polynomial

In mathematics, the Neumann polynomials, introduced by Carl Neumann for the special case

[1] The first few polynomials are A general form for the polynomial is and they have the "generating function" where J are Bessel functions.

An example is the extension or the more general Sonine formula[2] where

Then,[citation needed][original research?]

the confluent hypergeometric function and in particular the index shift formula the Taylor expansion (addition formula) (cf.

[3][failed verification]) and the expansion of the integral of the Bessel function, are of the same type.