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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} }}{...
Gary's user avatar
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7 votes

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)...
Carlo Beenakker's user avatar

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