Algebraic and Analytic Methods - 1.8 Fourier Series

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
1.8.E16	${\displaystyle{\displaystyle\sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega}={\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos\left(2n\pi x\right)\right)}}}$ \sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega} = {\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos@{2n\pi x}\right)}	${\displaystyle{\displaystyle\Re\omega>0}}$	sum(exp(-(n + x)^(2)* omega), n = - infinity..infinity) = sqrt((Pi)/(omega))*(1 + 2*sum(exp(- (n)^(2)* (Pi)^(2)/omega)*cos(2*n*Pi*x), n = 1..infinity))	Sum[Exp[-(n + x)^(2)* \[Omega]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sqrt[Divide[Pi,\[Omega]]]*(1 + 2*Sum[Exp[- (n)^(2)* (Pi)^(2)/\[Omega]]*Cos[2*n*Pi*x], {n, 1, Infinity}, GenerateConditions->None])	Failure	Successful	Successful [Tested: 15]	Successful [Tested: 15]