Legendre's Duplication Formula
\Gamma(s)\Gamma\left(s+\frac{1}{2}\right)=2\pi^\frac{1}{2}2^{-2s}\Gamma(2s)
Legendre’s Duplication Formula was first introduced by the French mathematician Adrien-Marie Legendre in 1811 as part of his work on the Gamma function.
This formula is particularly useful in simplifying expressions involving the Gamma Function, especially in integrals and series. It plays a role in various areas of mathematics, including number theory, complex analysis, and physics.
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