An Entry of Ramanujan on Hypergeometric Series in his Notebooks

K. Srinivasa Rao, G. Vanden Berghe, Christian Krattenthaler

Example 7, after Entry 43, in Chapter XII of the first Notebook of Srinivasa Ramanujan is proved and, more generally, a summation theorem for ${}_3{F}_2(a,a,x;1+a,1+a+N;1)$, where $N$…