$\sum_{m=1}^\infty \frac{1}{m} \bigg[{}_2F_1(-m,m,2,u)\bigg]^2 = \frac 1 4 -\frac 1 2 \log u$
I have very strong numerical support that this is true when $0<u\le1$. Can anyone help proving or disproving ?
Sum of squared hypergeometric polynomials
Matteo Beccaria
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