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Leopold Bernhard Gegenbauer
Leopold Bernhard Gegenbauer (2 February 1849, Asperhofen – 3 June 1903, Gießhübl) was an Austrian mathematician remembered best as an algebraist. Gegenbauer polynomials are named after him. Leopold Gegenbauer was the son of a doctor. He studied at the University of Vienna from 1869 until 1873. He then went to Berlin where he studied from 1873 to 1875 working under Weierstrass and Kronecker. After graduating from Berlin, Gegenbauer was appointed to the position of extraordinary professor at the University of Czernowitz in 1875. Czernowitz, on the upper Prut River in the Carpathian foothills, was at that time in the Austrian Empire but after World War I it was in Romania, then after 1944 it became Chernivtsi, Ukraine. Czernowitz University was founded in 1875 and Gegenbauer was the first professor of mathematics there. He remained in Czernowitz for three years before moving to the University of Innsbruck where he worked with Otto Stolz. Again he held the position of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gegenbauer
Gegenbauer is a German surname. Notable people with the surname include: *Josef Anton Gegenbauer (1800–1876), German historical and portrait painter *Leopold Gegenbauer (1849–1903), Austrian mathematician See also *Karl Gegenbaur (1826–1903), German anatomist and professor *Gegenbauer polynomials In mathematics, Gegenbauer polynomials or ultraspherical polynomials ''C''(''x'') are orthogonal polynomials on the interval minus;1,1with respect to the weight function (1 − ''x''2)''α''–1/2. They generalize Legendre polynomi ..., in mathematics {{surname, Gegenbauer German-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Pierpont (mathematician)
James P. Pierpont (June 16, 1866 – December 9, 1938) was a Connecticut-born American mathematician. His father Cornelius Pierpont was a wealthy New Haven businessman. He did undergraduate studies at Worcester Polytechnic Institute, initially in mechanical engineering, but turned to mathematics. He went to Europe after graduating in 1886. He studied in Berlin, and later in Vienna. He prepared his PhD at the University of Vienna under Leopold Gegenbauer and Gustav Ritter von Escherich. His thesis, defended in 1894, is entitled ''Zur Geschichte der Gleichung fünften Grades bis zum Jahre 1858''. After his defense, he returned to New Haven and was appointed as a lecturer at Yale University, where he spent most of his career. In 1898, he became professor. Initially, his research dealt with Galois theory of equations. The Pierpont primes are named after Pierpont, who introduced them in 1895 in connection with a problem of constructing regular polygons with the use of conic sectio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Austrian Mathematicians
Austrian may refer to: * Austrians, someone from Austria or of Austrian descent ** Someone who is considered an Austrian citizen, see Austrian nationality law * Austrian German dialect * Something associated with the country Austria, for example: ** Austria-Hungary ** Austrian Airlines (AUA) ** Austrian cuisine ** Austrian Empire ** Austrian monarchy ** Austrian German (language/dialects) ** Austrian literature ** Austrian nationality law ** Austrian Service Abroad ** Music of Austria ** Austrian School of Economics * Economists of the Austrian school of economic thought * The Austrian Attack variation of the Pirc Defence chess opening. See also * * * Austria (other) * Australian (other) * L'Autrichienne (other) is the feminine form of the French word , meaning "The Austrian". It may refer to: *A derogatory nickname for Queen Marie Antoinette of France *L'Autrichienne (film), ''L'Autrichienne'' (film), a 1990 French film on Marie Antoinette wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1903 Deaths
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1849 Births
Events January–March * January 1 – France begins issue of the Ceres series, the nation's first postage stamps. * January 5 – Hungarian Revolution of 1848: The Austrian army, led by Alfred I, Prince of Windisch-Grätz, enters in the Hungarian capitals, Buda and Pest. The Hungarian government and parliament flee to Debrecen. * January 8 – Hungarian Revolution of 1848: Romanian armed groups massacre 600 unarmed Hungarian civilians, at Nagyenyed.Hungarian HistoryJanuary 8, 1849 And the Genocide of the Hungarians of Nagyenyed/ref> * January 13 ** Second Anglo-Sikh War – Battle of Tooele: British forces retreat from the Sikhs. ** The Colony of Vancouver Island is established. * January 21 ** General elections are held in the Papal States. ** Hungarian Revolution of 1848: Battle of Nagyszeben – The Hungarian army in Transylvania, led by Josef Bem, is defeated by the Austrians, led by Anton Puchner. * January 23 – Elizabeth Blackwell is awarded her M.D. by the Medi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floridsdorf
Floridsdorf (; Central Bavarian: ''Fluridsduaf'') is the 21st district of Vienna (german: 21. Bezirk, Floridsdorf), located in the northern part of the city and comprising seven formerly independent communities: Floridsdorf, Donaufeld, Greater Jedlersdorf, Jedlesee, Leopoldau, Stammersdorf, and Strebersdorf. History Prehistory Settlements were already present during the New Stone Age (4000 to 2000 BC). Stone axes and potsherds unearthed from that time indicate that the first settlers in the area were hunters. In the vicinity of Leopoldau, bronze weapons and jewelry provide evidence of subsequent settlement. Several of these items are now in the District Museum. Early history Around 500 BC, Celts entered the territory of present-day Floridsdorf, losing ground to the Romans as their empire expanded. The territory became a no-man's-land, or buffer zone, between the Romans and teutonic tribes, during a period when repeated battles were fought between the two peoples. After the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Number Theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet ''L''-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem). Branches of analytic number theory Analytic number theory can be split up into two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique. *Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval, and includes the prime number theorem and Dirichlet's theorem on primes in arithmetic progressions. *Additive number th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Associated Legendre Polynomial
In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equation \left(1 - x^2\right) \frac P_\ell^m(x) - 2 x \frac P_\ell^m(x) + \left \ell (\ell + 1) - \frac \rightP_\ell^m(x) = 0, or equivalently \frac \left \left(1 - x^2\right) \frac P_\ell^m(x) \right+ \left \ell (\ell + 1) - \frac \rightP_\ell^m(x) = 0, where the indices ''ℓ'' and ''m'' (which are integers) are referred to as the degree and order of the associated Legendre polynomial respectively. This equation has nonzero solutions that are nonsingular on only if ''ℓ'' and ''m'' are integers with 0 ≤ ''m'' ≤ ''ℓ'', or with trivially equivalent negative values. When in addition ''m'' is even, the function is a polynomial. When ''m'' is zero and ''ℓ'' integer, these functions are identical to the Legendre polynomials. In general, when ''ℓ'' and ''m'' are integers, the regular solutions are sometimes called "associated Legendre polynomials", even though they are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Polynomials
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonality, orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The Gegenbauer polynomials form the most important class of Jacobi polynomials; they include the Chebyshev polynomials, and the Legendre polynomials as special cases. The field of orthogonal polynomials developed in the late 19th century from a study of continued fractions by Pafnuty Chebyshev, P. L. Chebyshev and was pursued by Andrey Markov, A. A. Markov and Thomas Joannes Stieltjes, T. J. Stieltjes. They appear in a wide variety of fields: numerical analysis (Gaussian quadrature, quadrature rules), probability theory, representation theory (of Lie group, Lie groups, quantum group, quantum groups, and re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics. By extension, use of complex analysis also has applications in engineering fields such as nuclear engineering, nuclear, aerospace engineering, aerospace, mechanical engineering, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to its Taylor series (that is, it is Analyticity of holomorphic functions, analytic), complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions). History Complex analysis is one of the classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
