Hjalmar Mellin

Robert Hjalmar Mellin (1854–1933), a Finnish function-theorist. He studied in Helsinki University under Gösta Mittag-Leffler, in Berlin under Karl Weierstrass and Leopold Kronecker. He worked as professor of mathematics in the Helsinki Polytechnic Institute (later the Technical University of Finland).

Mellin is best known for his integral transform, the Mellin transform (http://planetmath.org/MellinTransform)

$$F(s):={\int }_0^{\mathrm{\infty }}{t}^{s-1}f(t)𝑑t,$$

which he utilised in study of gamma function, hypergeometric functions, Dirichlet series, Riemann zeta function and related number-theoretic functions. Mellin’s transform and its inverse transform

$$f(t)=\frac{1}{2\pi i}{\int }_{a-i\mathrm{\infty }}^{a+i\mathrm{\infty }}{t}^{-z}F(z)𝑑z$$

are much used also in physics. Mellin himself applied his transformations for solving partial differential equations and the inverse transformations for forming asymptotic series expansions.

Mellin has addressed of relativity.

Title	Hjalmar Mellin
Canonical name	HjalmarMellin
Date of creation	2015-02-17 14:49:42
Last modified on	2015-02-17 14:49:42
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	8
Author	pahio (2872)
Entry type	Biography
Classification	msc 01A55
Classification	msc 01A60
Synonym	Mellin
Related topic	MellinsInverseFormula