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n-a-n-n-1-2-b-n-n-1-2-1-2a-2-pi-0-e-t-2-2-1-a-ab-cosh-log-ab-t-a-3-b-2a-ab-cosh-log-ab-t-dt-




Question Number 136850 by Dwaipayan Shikari last updated on 26/Mar/21
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
n=an(n+1)2bn(n1)2=1+2a2π0et2/2(1aabcosh(log(ab)t)a3b2aabcosh(log(ab)t))dt
Commented by Dwaipayan Shikari last updated on 26/Mar/21
I have found this on Wikipedia . Any idea how to prove?
IhavefoundthisonWikipedia.Anyideahowtoprove?

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