Σ_(n=−∞) ^∞ a^((n(n+1))/2) b^((n(n−1))/2) =1+(√((2a^2 )/π))∫_0 ^∞ e^(−t^2 /2) (((1−a(√(ab)) cosh((√(log(ab))) t))/(a^3 b−2a(√(ab )) cosh((√(log(ab))) t))))dt


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Question Number 136850 by Dwaipayan Shikari last updated on 26/Mar/21

$\underset{n = - \infty}{\sum^{\infty}} a^{\frac{n (n + 1)}{2}} b^{\frac{n (n - 1)}{2}} = 1 + \sqrt{\frac{2 a^{2}}{π}} \int_{0}^{\infty} e^{- t^{2} / 2} (\frac{1 - a \sqrt{a b} c o s h (\sqrt{l o g (a b)} t)}{a^{3} b - 2 a \sqrt{a b} c o s h (\sqrt{l o g (a b)} t)}) d t$
Commented by Dwaipayan Shikari last updated on 26/Mar/21

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