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| Robert Hjalmar Mellin (1854--1933), a Finnish function-theorist. He studied in Helsinki University under G\"osta 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). |
Robert Hjalmar Mellin (1854--1933), a Finnish function-theorist. He studied in Helsinki University under G\"osta 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). |
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| Mellin is best known for his integral transform, the {\em Mellin transformation} |
Mellin is best known for his integral transform, the {\em Mellin transformation} |
| $$F(s) := \int_0^\infty t^{s-1}f(t)\,dt,$$ |
$$F(s) := \int_0^\infty t^{s-1}f(t)\,dt,$$ |
| 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 |
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 |
| $$f(t) = \frac{1}{2\pi i}\int_{a-i\infty}^{a+i\infty}t^{-z}F(z)\,dz$$ |
$$f(t) = \frac{1}{2\pi i}\int_{a-i\infty}^{a+i\infty}t^{-z}F(z)\,dz$$ |
| 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. |
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. |
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| Mellin has addressed \PMlinkescapetext{strict criticism to the foundations of Einstein's theory} of relativity. |
Mellin has addressed \PMlinkescapetext{strict criticism to the foundations of Einstein's theory} of relativity. |
