(1/(1+(η^2 /(1+(((η+1)^2 )/(1+(((η+2)^2 )/(1+(((η+3)^2 )/(1+..)) ))))))))=(1/2)ψ(((η+2)/2))−(1/2)ψ(((η+1)/2)) (η>0) Or K_(r=0) ^∞ (η+r)^2 =(2/(ψ((η/2)+1)−ψ(((η+1)/2))))


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Question Number 136645 by Dwaipayan Shikari last updated on 24/Mar/21

$\frac{1}{1 + \frac{η^{2}}{1 + \frac{{(η + 1)}^{2}}{1 + \frac{{(η + 2)}^{2}}{1 + \frac{{(η + 3)}^{2}}{1 + . .}}}}} = \frac{1}{2} ψ (\frac{η + 2}{2}) - \frac{1}{2} ψ (\frac{η + 1}{2}) (η > 0)$ $O r \underset{r = 0}{\overset{\infty}{K}} {(η + r)}^{2} = \frac{2}{ψ (\frac{η}{2} + 1) - ψ (\frac{η + 1}{2})}$
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