Question Number 36751 by prof Abdo imad last updated on 05/Jun/18
![let f(x)= Σ_(n=1) ^∞ x^n^2 with x∈]−1,1[ prove that f(x) ∼ ((√π)/(2(√(−ln(x))))) (x →1^− )](https://www.tinkutara.com/question/Q36751.png)
$$\left.{let}\:\:{f}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{x}^{{n}^{\mathrm{2}} } \:\:\:{with}\:\:{x}\in\right]−\mathrm{1},\mathrm{1}\left[\right. \\ $$$${prove}\:{that}\:\:{f}\left({x}\right)\:\sim\:\frac{\sqrt{\pi}}{\mathrm{2}\sqrt{−{ln}\left({x}\right)}}\:\left({x}\:\rightarrow\mathrm{1}^{−} \right) \\ $$