(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate $P\int_{-\infty}^{\infty}\exp(imx^2}dx$, $m>0$.

2. Relevant equations

None

3. The attempt at a solution

Consider the following contour $C$ consisting of

$C_1:=\{z=x+iy:y=0, x:-s \to s\}$

$C_2:=\{z=x+iy:x=0, y:0 \to is\}$

$C_3:=\{z=x+iy:x: s \to -s, y: is \to -is \}$

$C_4:=\{z=x+iy:x=0: y:-is \to 0\}$

This is where i am stuck

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Rieman Zeta

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