multiplication theorem

Summary

multiplication theorem is a theorem^[1]. It draws 42 Wikipedia views per month (theorem category, ranking #235 of 1,306).^[2]

Key Facts

• multiplication theorem's instance of is recorded as theorem^[3].
• multiplication theorem's part of is recorded as list of theorems^[4].
• multiplication theorem's Freebase ID is recorded as /m/027g78j^[5].
• multiplication theorem's defining formula is recorded as \frac{d \xi}{d t} + \nabla \cdot f(\xi) = 0^[6].
• multiplication theorem's defining formula is recorded as \Gamma (z)\;\Gamma \left(z+{\frac {1}{2}}\right)=2^{{1-2z}}\;{\sqrt {\pi }}\;\Gamma (2z).\,!^[7].
• multiplication theorem's defining formula is recorded as \Gamma (z)\;\Gamma \left(z+{\frac {1}{k}}\right)\;\Gamma \left(z+{\frac {2}{k}}\right)\cdots \Gamma \left(z+{\frac {k-1}{k}}\right)=(2\pi )^{{{\frac {k-1}{2}}}}\;k^{{1/2-kz}}\;\Gamma (kz)\,!^[8].
• multiplication theorem's defining formula is recorded as k^{{m}}\psi ^{{(m-1)}}(kz)=\sum _{{n=0}}^{{k-1}}\psi ^{{(m-1)}}\left(z+{\frac {n}{k}}\right)^[9].
• multiplication theorem's defining formula is recorded as k\left[\psi (kz)-\log(k)\right]=\sum _{{n=0}}^{{k-1}}\psi \left(z+{\frac {n}{k}}\right).^[10].
• multiplication theorem's defining formula is recorded as k^{s}\zeta (s)=\sum _{{n=1}}^{k}\zeta \left(s,{\frac {n}{k}}\right),^[11].
• multiplication theorem's defining formula is recorded as k^{s}\,\zeta (s,kz)=\sum _{{n=0}}^{{k-1}}\zeta \left(s,z+{\frac {n}{k}}\right)^[12].
• multiplication theorem's defining formula is recorded as \zeta (s,kz)=\sum _{{n=0}}^{{\infty }}{s+n-1 \choose n}(1-k)^{n}z^{n}\zeta (s+n,z).^[13].
• multiplication theorem's defining formula is recorded as F(s;q)=\sum {{m=1}}^{\infty }{\frac {e^{{2\pi imq}}}{m^{s}}}=\operatorname {Li}{s}\left(e^{{2\pi iq}}\right)^[14].
• multiplication theorem's defining formula is recorded as 2^{{-s}}F(s;q)=F\left(s,{\frac {q}{2}}\right)+F\left(s,{\frac {q+1}{2}}\right).^[15].
• multiplication theorem's defining formula is recorded as k^{{-s}}F(s;kq)=\sum _{{n=0}}^{{k-1}}F\left(s,q+{\frac {n}{k}}\right).^[16].
• multiplication theorem's maintained by WikiProject is recorded as WikiProject Mathematics^[17].
• multiplication theorem's Microsoft Academic ID is recorded as 75090586^[18].

Why It Matters

multiplication theorem draws 42 Wikipedia views per month (theorem category, ranking #235 of 1,306).^[2]