The evaluation of a weighted sum of Gauss hypergeometric functions and its connection with Galton-Watson processes

R B Paris, Vladimir V Vinogradov

We evaluate the sum of Gauss hypergeometric functions \[S(μ,c;x)=\sum_{k\geq 0} \bl(\frac{1-x}{1+μ}\br)^k\,{}_2F_1(\fs k+\fs, \fs k+1;c;x)\] for $x\in [-1,1]$ and positive paramete…