edgepedia

Special functions and classical ODE researchers

28 articles

Adolf Kneser

Adolf Kneser (1862–1930) was a German mathematician who worked on the calculus of variations and linear differential equations, bringing Sturm–Liouville eigenfunction expansions to Dirichlet-level generality.

Alfred Cardew Dixon

Alfred Cardew Dixon (1865–1936) was an English mathematician, Senior Wrangler at Cambridge in 1886, remembered for Dixon's identity, the Dixon elliptic functions, and early work on Fredholm integral equations.

Arthur Erdélyi

Arthur Erdélyi (1908–1977) was a Hungarian-born British mathematician, a leading authority on special functions and asymptotic analysis who directed the five-volume Bateman Manuscript Project at Caltech.

Carl Neumann

Carl Gottfried Neumann was a Prussian mathematician who solved the first and second boundary value problems for the Laplace equation, co-founded Mathematische Annalen, and held Leipzig's chair for 43 years.

Charles Fox (mathematician)

Charles Fox (1897–1977) was an English-born Canadian mathematician who taught at McGill University in Montreal and introduced the Fox H-function, used in fractional calculus and wireless engineering.

Cornelis Simon Meijer

Cornelis Simon Meijer (1904–1974) was a Dutch mathematician at the University of Groningen who introduced the Meijer G-function in 1936, a Mellin–Barnes integral generalizing hypergeometric functions.

Edward Lindsay Ince

Edward Lindsay Ince (1891–1941) was a British mathematician who worked on ordinary differential equations, the Mathieu and Lamé functions, and published the 1932 tables of Mathieu's equation.

G. N. Watson

G. N. Watson, George Neville Watson, was an English mathematician who wrote the standard treatise on Bessel functions, co-authored Modern Analysis with Whittaker, and proved the Rogers–Ramanujan identities.

Hans Hamburger

Hans Ludwig Hamburger (1889–1956) was a German mathematician known for the Hamburger moment problem, extending the Stieltjes moment problem to the whole real line in 1920–21.

Harold Exton

Harold Exton (born 20 June 1928) is a mathematician who wrote books on multiple and q-hypergeometric functions, including q-Hypergeometric Functions and Applications (1983), and whose name is attached to the Hahn–Exton q-Bessel function.

Hermann Kober

Hermann Kober (1888–1973) was a German-born mathematician who worked in England and is known for Kober's Theorem in Banach-space theory and the Erdélyi–Kober fractional operators.

Johannes Mollerup

Johannes Mollerup (1872–1937) was a Danish mathematician, professor at the Technical University of Denmark from 1916, known for the Bohr–Mollerup theorem and the Danish analysis textbook he wrote with Harald Bohr.

Karl Heun

Karl Heun (1859–1929) was a German mathematician who introduced Heun's equation, a second-order differential equation generalizing the hypergeometric equation, and Heun's 1900 method, an early step in the Runge–Kutta lineage.

Lazarus Fuchs

Lazarus Immanuel Fuchs (1833–1902) was a German mathematician, a pupil of Weierstrass, who characterized the Fuchsian class of linear differential equations; Poincaré named Fuchsian functions in his honor.

Leo August Pochhammer

Leo August Pochhammer (1841–1920) was a German mathematician who taught at the University of Kiel and is known for the Pochhammer symbol, the Pochhammer function, and the generalized hypergeometric function.

Mary Cartwright

Dame Mary Lucy Cartwright was a British mathematician known for work on complex function theory and, with J. E. Littlewood, an early discovery of chaos in the forced van der Pol equation.

Morris Marden

Morris Marden (1905–1991) was an American mathematician who studied the geometry of polynomial zeros, wrote the monograph Geometry of Polynomials, and built the graduate program at the University of Wisconsin–Milwaukee.

Oscar Schlömilch

Oscar Schlömilch (1823–1901) was a German mathematician, professor in Dresden, founding editor of the Zeitschrift für Mathematik und Physik, and namesake of the Schlömilch series, an 1857 expansion in Bessel functions.

Oskar Perron

Oskar Perron (1880–1975) was a German mathematician who held chairs at Heidelberg and Munich and is known for the Perron–Frobenius theorem, the Perron integral, and continued fractions.

Paul Appell

Paul Appell (1855–1930) was a French mathematician from Strasbourg who introduced the Appell functions F1–F4 and Appell polynomials, and led the University of Paris as dean and rector.

Paul Painlevé

Paul Painlevé (1863–1933) was a French mathematician and statesman who discovered the Painlevé transcendents and served twice as prime minister of France, in 1917 and 1925.

Philip Hartman

Philip Hartman (1915–2015) was an American mathematician at Johns Hopkins University who worked on ordinary differential equations, proved the Hartman–Grobman theorem, and wrote the textbook Ordinary Differential Equations.

Rudolf Lipschitz

Rudolf Lipschitz (1832–1903) was a German mathematician, professor at Bonn from 1864, whose Lipschitz condition underlies uniqueness proofs for differential equations and whose work anticipated relativity and spinor theory.

Thomas Hakon Grönwall

Thomas Hakon Grönwall, born Hakon Tomi Grönwall, was a Swedish-born American mathematician (1877–1932) known for the 1919 Grönwall inequality, a summability method for series, and work on Fourier series.

Thomas Murray MacRobert

Thomas Murray MacRobert (1884–1962) was a Scottish mathematician and Professor of Mathematics at the University of Glasgow, known for his work on the hypergeometric function and the E-function.

Vladimir Ivanovich Mironenko

Vladimir Ivanovich Mironenko (Владимир Иванович Мироненко; born 1942) is a Belarusian mathematician known for introducing the reflecting function, a tool for studying periodic solutions of differential systems.

William A. Coppel

William A. Coppel, full name William Andrew Coppel, was a mathematician who worked on ordinary differential equations, stability theory, and dichotomies at the Australian National University.

Zdzisław Opial

Zdzisław Opial (1930–1974) was a Polish mathematician at the Jagiellonian University in Kraków, known for Opial's inequality, a fundamental integral inequality in the qualitative theory of differential equations.