New answers tagged gamma-function
0
votes
Stirling's formula and a Gamma function relation
Denote your fraction by $R(s)$. By the duplication formula,
$$
\Gamma\! \left( {s - \frac{1}{2}} \right) = \Gamma \!\left( {2\left( {\frac{s}{2} - \frac{1}{4}} \right)} \right) = \frac{{2^{s - 3/2} }}{...
- 188
7
votes
Accepted
New method to compute square roots
Let me "unclutter" the basic formula $S(x,a)=\sqrt{x}$, starting from the definition in the OP,
$$S(x,a) =\sum_{n=0}^{\infty}\left(\frac{\left(n+1\right)\binom{2n+2}{n+1}}{\left(4n^2-1\right)...
- 163k
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