DLMF:1.8.E16 (Q270): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
Property / constraint
 

ω > 0 𝜔 0 {\displaystyle{\displaystyle\Re\omega>0}}

\realpart@@{\omega}>0
Property / constraint: ω > 0 𝜔 0 {\displaystyle{\displaystyle\Re\omega>0}} / rank
 
Normal rank

Revision as of 15:48, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:1.8.E16
No description defined

    Statements

    n = - e - ( n + x ) 2 ω = π ω ( 1 + 2 n = 1 e - n 2 π 2 / ω cos ( 2 n π x ) ) , superscript subscript 𝑛 superscript 𝑒 superscript 𝑛 𝑥 2 𝜔 𝜋 𝜔 1 2 superscript subscript 𝑛 1 superscript 𝑒 superscript 𝑛 2 superscript 𝜋 2 𝜔 2 𝑛 𝜋 𝑥 {\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)},}}
    0 references
    0 references
    ω > 0 𝜔 0 {\displaystyle{\displaystyle\Re\omega>0}}
    0 references