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Hjalmar Mellin (Biography)

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 transformation

$\displaystyle F(s) := \int_0^\infty t^{s-1}f(t)\,dt,$
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
$\displaystyle f(t) = \frac{1}{2\pi i}\int_{a-i\infty}^{a+i\infty}t^{-z}F(z)\,dz$
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 strict criticism to the foundations of Einstein's theory of relativity.



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See Also: Mellin's inverse formula

Other names:  Mellin
Keywords:  function theory
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Cross-references: series, partial differential equations, Transform, Mellin's transform, functions, Riemann zeta function, Dirichlet series, hypergeometric functions, gamma function, transformation, integral transform, Karl Weierstrass
There are 3 references to this entry.

This is version 3 of Hjalmar Mellin, born on 2008-01-19, modified 2008-01-22.
Object id is 10201, canonical name is HjalmarMellin.
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Classification:
AMS MSC: 01A55 (History and biography :: History of mathematics and mathematicians :: 19th century)
 01A60 (History and biography :: History of mathematics and mathematicians :: 20th century)
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