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Wolfgang Hahn
Wolfgang Hahn (April 30, 1911 – January 10, 1998) was a German mathematician who worked on special functions, in particular orthogonal polynomials. He introduced Hahn polynomials, Hahn difference, Hahn q-addition (or Jackson-Hahn-Cigler q-addition), and the Hahn–Exton q-Bessel function. He was an honorary member of the Austrian Mathematical Society The Austrian Mathematical Society (german: Österreichische Mathematische Gesellschaft) is the national mathematical society of Austria and a member society of the European Mathematical Society. History The society was founded in 1903 by Ludwig B .... References * * * External links *Pictures of Wolfgang Hahn from Oberwolfach {{DEFAULTSORT:Hahn, Wolfgang 1911 births 1998 deaths Academic staff of the Technical University of Braunschweig 20th-century German mathematicians Q-analogs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potsdam
Potsdam () is the capital and, with around 183,000 inhabitants, largest city of the German state of Brandenburg. It is part of the Berlin/Brandenburg Metropolitan Region. Potsdam sits on the River Havel, a tributary of the Elbe, downstream of Berlin, and lies embedded in a hilly morainic landscape dotted with many lakes, around 20 of which are located within Potsdam's city limits. It lies some southwest of Berlin's city centre. The name of the city and of many of its boroughs are of Slavic origin. Potsdam was a residence of the Prussian kings and the German Kaiser until 1918. Its planning embodied ideas of the Age of Enlightenment: through a careful balance of architecture and landscape, Potsdam was intended as "a picturesque, pastoral dream" which would remind its residents of their relationship with nature and reason. The city, which is over 1000 years old, is widely known for its palaces, its lakes, and its overall historical and cultural significance. Landmarks inclu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hyp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Staff Of The Technical University Of Braunschweig
An academy ( Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy, founded approximately 385 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and skill, north of Athens, Greece. Etymology The word comes from the ''Academy'' in ancient Greece, which derives from the Athenian hero, '' Akademos''. Outside the city walls of Athens, the gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive grove, hence the expression "the groves of Academe". In these gardens, the philosopher Plato conversed with followers. Plato developed his sessions into a method of teaching philosophy and in 387 BC, established what is known today as the Old Academy. By extension, ''academia'' has come to mean the accumulatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1998 Deaths
This is a list of deaths of notable people, organised by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked here. 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 See also * Lists of deaths by day * Deaths by year {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1911 Births
A notable ongoing event was the Comparison of the Amundsen and Scott Expeditions, race for the South Pole. Events January * January 1 – A decade after federation, the Northern Territory and the Australian Capital Territory are added to the Commonwealth of Australia. * January 3 ** 1911 Kebin earthquake: An earthquake of 7.7 Moment magnitude scale, moment magnitude strikes near Almaty in Russian Turkestan, killing 450 or more people. ** Siege of Sidney Street in London: Two Latvian people, Latvian anarchists die, after a seven-hour siege against a combined police and military force. Home Secretary Winston Churchill arrives to oversee events. * January 5 – Egypt's Zamalek SC is founded as a general sports and Association football club by Belgian lawyer George Merzbach as Qasr El Nile Club. * January 14 – Roald Amundsen's South Pole expedition makes landfall, on the eastern edge of the Ross Ice Shelf. * January 18 – Eugene B. El ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Austrian Mathematical Society
The Austrian Mathematical Society (german: Österreichische Mathematische Gesellschaft) is the national mathematical society of Austria and a member society of the European Mathematical Society. History The society was founded in 1903 by Ludwig Boltzmann, Gustav von Escherich and Emil Müller as ''Mathematical Society in Vienna'' (german: Mathematische Gesellschaft in Wien). After the Second World War it resumed operation in May 1946 and was formally reestablished at the 10th of August 1946 by Rudolf Inzinger. In autumn 1948 the name was changed to ''Austrian Mathematical Society''. Publications It publishes the "International Mathematical News" (german: Internationale Mathematische Nachrichten) with three issues per year (not to be confused with ''Mathematische Nachrichten'', an unrelated mathematics journal). It was issued for the first time in 1947. It also publishes the mathematics journal ''Monatshefte für Mathematik'' in cooperation with Springer-Verlag Springer Scie ... [...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 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 P. L. Chebyshev and was pursued by A. A. Markov and T. J. Stieltjes. They appear in a wide variety of fields: numerical analysis ( quadrature rules), probability theory, representation theory (of Lie groups, quantum groups, and related objects), enumerative combinatorics, algebraic combinatorics, mathematical physics (the theory of random matr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Functions
Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by consensus, and thus lacks a general formal definition, but the List of mathematical functions contains functions that are commonly accepted as special. Tables of special functions Many special functions appear as solutions of differential equations or integrals of elementary functions. Therefore, tables of integrals usually include descriptions of special functions, and tables of special functions include most important integrals; at least, the integral representation of special functions. Because symmetries of differential equations are essential to both physics and mathematics, the theory of special functions is closely related to the theory of Lie groups and Lie algebras, as well as certain topics in mathematical physics. Symbol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hahn–Exton Q-Bessel Function
In mathematics, the Hahn–Exton ''q''-Bessel function or the third Jackson q-Bessel function, Jackson ''q''-Bessel function is a q-analog, ''q''-analog of the Bessel function, and satisfies the Hahn-Exton ''q''-difference equation (). This function was introduced by in a special case and by in general. The Hahn–Exton ''q''-Bessel function is given by : J_\nu^(x;q) = \frac \sum_\frac= \frac x^\nu _1\phi_1(0;q^;q,qx^2). \phi is the basic hypergeometric function. Properties Zeros Koelink and Swarttouw proved that J_\nu^(x;q) has infinite number of real zeros. They also proved that for \nu>-1 all non-zero roots of J_\nu^(x;q) are real (). For more details, see and . Zeros of the Hahn-Exton ''q''-Bessel function appear in a discrete analog of Daniel Bernoulli's problem about free vibrations of a lump loaded chain (, ) Derivatives For the (usual) derivative and ''q''-derivative of J_\nu^(x;q), see . The symmetric ''q''-derivative of J_\nu^(x;q) is described on . Recurrence R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kassel
Kassel (; in Germany, spelled Cassel until 1926) is a city on the Fulda River in northern Hesse, Germany. It is the administrative seat of the Regierungsbezirk Kassel and the district of the same name and had 201,048 inhabitants in December 2020. The former capital of the state of Hesse-Kassel has many palaces and parks, including the Bergpark Wilhelmshöhe, which is a UNESCO World Heritage Site. Kassel is also known for the ''documenta'' exhibitions of contemporary art. Kassel has a public university with 25,000 students (2018) and a multicultural population (39% of the citizens in 2017 had a migration background). History Kassel was first mentioned in 913 AD, as the place where two deeds were signed by King Conrad I. The place was called ''Chasella'' or ''Chassalla'' and was a fortification at a bridge crossing the Fulda river. There are several yet unproven assumptions of the name's origin. It could be derived from the ancient ''Castellum Cattorum'', a castle of the C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hahn Polynomials
In mathematics, the Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials, introduced by Pafnuty Chebyshev in 1875 and rediscovered by Wolfgang Hahn . The Hahn class is a name for special cases of Hahn polynomials, including Hahn polynomials, Meixner polynomials, Krawtchouk polynomials, and Charlier polynomials. Sometimes the Hahn class is taken to include limiting cases of these polynomials, in which case it also includes the classical orthogonal polynomials. Hahn polynomials are defined in terms of generalized hypergeometric functions by :Q_n(x;\alpha,\beta,N)= _3F_2(-n,-x,n+\alpha+\beta+1;\alpha+1,-N+1;1).\ give a detailed list of their properties. If \alpha = \beta = 0, these polynomials are identical to the discrete Chebyshev polynomials except for a scale factor. Closely related polynomials include the dual Hahn polynomials In mathematics, the dual Hahn polynomials are a family of orthogonal polynomials ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Issai Schur
Issai Schur (10 January 1875 – 10 January 1941) was a Russian mathematician who worked in Germany for most of his life. He studied at the University of Berlin. He obtained his doctorate in 1901, became lecturer in 1903 and, after a stay at the University of Bonn, professor in 1919. As a student of Ferdinand Georg Frobenius, he worked on group representations (the subject with which he is most closely associated), but also in combinatorics and number theory and even theoretical physics. He is perhaps best known today for his result on the existence of the Schur decomposition and for his work on group representations (Schur's lemma). Schur published under the name of both I. Schur, and J. Schur, the latter especially in ''Journal für die reine und angewandte Mathematik''. This has led to some confusion. Childhood Issai Schur was born into a Jewish family, the son of the businessman Moses Schur and his wife Golde Schur (née Landau). He was born in Mogilev on the Dnieper R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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