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Tagged with combinatorial-identities closed-form-expressions
2 questions
0
votes
1
answer
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Closed form of a Hypergeometric Function ${}_2F_1$ at $z=-8$
How this can be proved?
$$
E = {}_2F_1(-\frac{1}{2}, \frac{1}{3}, \frac{4}{3},-8) = \frac{6}{5} - \frac{\chi}{2}
$$
where
$$
\chi = \frac{6\sqrt{\pi}}{5}\frac{\Gamma(\frac{1}{3})}{\Gamma(-\frac{1}{6})}...
2
votes
0
answers
376
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Reflection formula for the Hurwitz zeta function and odd zeta values
A reflection formula for the Hurwitz zeta function, which does not seem to be well known, uses half of the polynomials generated by $\frac{1}{-1+\sqrt{t-1}\cot(\sqrt{t-1}u)}$. (Look at the sections "...
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