Published 04-03-2025
Keywords
- Euler transform,
- Hypergeometric function,
- functional identity
Abstract
A new proof is presented for an old algebraic identity which is then used to produce the general functional relation
\(\ sum_{k=0}^{n-1} \frac{(m)_k}{k!} g(m,k) + \sum_{k=0}^{m-1} \frac{(n)_k}{k!} g(k,n) = g(0,0)\)
where \(\ g\) is an Euler transform, and a related integral identity. Several examples are given.
