Mellin Transform

$\displaystyle \phi(z)$	$\textstyle =$	$\displaystyle \int^\infty_0 t^{z-1}f(t)\,dt$
$\displaystyle f(t)$	$\textstyle =$	$\displaystyle {1\over 2\pi i} \int_{-\infty}^\infty t^{-z}\phi (z)\,dz.$

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 795, 1985.

Bracewell, R. The Fourier Transform and Its Applications. New York: McGraw-Hill, pp. 254-257, 1965.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 469-471, 1953.