Mellin Transform

An integral transform mapping a function f(r) on the positive half-line to F(s) = ∫_0^∞ r^{s-1} f(r) dr, converting dilation (scaling) behavior near r = 0 or ∞ into meromorphic dependence on the complex parameter s; extensively used to analyze singularities and boundary asymptotics, especially near conical points.