Convergence of f_{n} (x) = π*x*exp(-πx) on (0,∞)

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Sequence converge uniformly?

Homework Statement



Define f_{n}: (0,∞) → R, through f_{n} (x) = π*x*exp(-πx), x > 0.
Does the sequence converge uniformly in (0,∞) when n → ∞?

f_{n} = f subscript n

Can somebody please show me all the steps? Any ideas where i can start?
 
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Is the Uniform convergence theorem a good approach?
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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