The Cauchy-Schlomilch transformation

T. Amdeberhan, M. L. Glasser, M. C. Jones +3

The Cauchy-Schlömilch transformation states that for a function $f$ and $a,b>0$, the integral of $f(x^2)$ and $af((ax-b{x}^{-1}{)}^2$ over the interval $[0,\infty )$ are the…