Gamma duplication formula
= Gamma duplication formula
$$
\Gamma(z)\Gamma(z+\tfrac12)=2^{1-2z}\sqrt\pi\,\Gamma(2z).
$$
It follows by making the logarithm of the quotient entire and periodic; growth forces its periodic remainder to be constant.
= Gamma duplication formula
$$
\Gamma(z)\Gamma(z+\tfrac12)=2^{1-2z}\sqrt\pi\,\Gamma(2z).
$$
It follows by making the logarithm of the quotient entire and periodic; growth forces its periodic remainder to be constant.