Published 2019-08-27
Keywords
- Euler transform,
- Hypergeometric function,
- functional identity
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
A small trove of functional equations. (2019). Scientia Series A: Mathematical Sciences, 29, 61-63. https://revistas.usm.cl/scientia/article/view/48
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.
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