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Carl Severin Wigert
Carl Severin Wigert (1871–1941) was a Swedish mathematician who created Stieltjes–Wigert polynomials and worked on the divisor function In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as ''the'' divisor function, it counts the ''number of divisors of an integer'' (includi ..., including correctly describing its maximal order of growth. Wigert proved that :\limsup_\frac=\log2. Selected publications * * References * 20th-century Swedish mathematicians 1871 births 1941 deaths {{Sweden-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Swedish People
Swedes (), or Swedish people, are an ethnic group native to Sweden, who share a common ancestry, Culture of Sweden, culture, History of Sweden, history, and Swedish language, language. They mostly inhabit Sweden and the other Nordic countries, Swedish-speaking population of Finland, in particular, neighboring Finland, where they are an officially recognized minority, with Swedish being one of the official languages of the country, and with a substantial Swedish diaspora, diaspora in other countries, especially the Swedish Americans, United States. Etymology The English term "Swede" has been attested in English since the late 16th century and is of Middle Dutch or Middle Low German origin. In Swedish language, Swedish, the term is ''svensk'', which is from the name of ''svear'' (or Swedes), the people who inhabited Svealand in eastern central Sweden, and were listed as ''Suiones'' in Tacitus' history ''Germania (book), Germania'' from the first century AD. The term is believed ... [...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, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); 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's theorem. The number of known mathematicians grew when Pythagoras of Samos () 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 math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stieltjes–Wigert Polynomials
In mathematics, Stieltjes–Wigert polynomials (named after Thomas Jan Stieltjes and Carl Severin Wigert) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, for the weight function : w(x) = \frac x^ \exp(-k^2\log^2 x) on the positive real line ''x'' > 0. The moment problem for the Stieltjes–Wigert polynomials is indeterminate; in other words, there are many other measures giving the same family of orthogonal polynomials (see Krein's condition). Koekoek et al. (2010) give in Section 14.27 a detailed list of the properties of these polynomials. Definition The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol byUp to a constant factor ''S''''n''(''x'';''q'')=''p''''n''(''q''−1/2''x'') for ''p''''n''(''x'') in Szegő (1975), Section 2.7. :\displaystyle S_n(x;q) = \frac_1\phi_1(q^,0;q,-q^x), where : q = \exp \left(-\frac \right) . Orthogonality Since the moment problem In mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divisor Function
In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as ''the'' divisor function, it counts the ''number of divisors of an integer'' (including 1 and the number itself). It appears in a number of remarkable identities, including relationships on the Riemann zeta function and the Eisenstein series of modular forms. Divisor functions were studied by Ramanujan, who gave a number of important congruences and identities; these are treated separately in the article Ramanujan's sum. A related function is the divisor summatory function, which, as the name implies, is a sum over the divisor function. Definition The sum of positive divisors function ''σ''''z''(''n''), for a real or complex number ''z'', is defined as the sum of the ''z''th powers of the positive divisors of ''n''. It can be expressed in sigma notation as :\sigma_z(n)=\sum_ d^z\,\! , where is shorthand fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is a deductive reasoning, deductive Argument-deduction-proof distinctions, argument for a Proposition, mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning that establish logical certainty, to be distinguished from empirical evidence, empirical arguments or non-exhaustive inductive reasoning that establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1871 Births
Events January–March * January 3 – Franco-Prussian War: Battle of Bapaume – Prussians win a strategic victory. * January 18 – Proclamation of the German Empire: The member states of the North German Confederation and the south German states unite into a single nation state, known as the German Empire. The King of Prussia is declared the first German Emperor as Wilhelm I of Germany, in the Hall of Mirrors at the Palace of Versailles. The Constitution of the German Confederation comes into effect. It abolishes all restrictions on Jewish marriage, choice of occupation, place of residence, and property ownership, but exclusion from government employment and discrimination in social relations remain in effect. * January 21 – Battle of Dijon: Giuseppe Garibaldi's group of French and Italian volunteer troops, in support of the French Third Republic, win a battle against the Prussians. * February 8 – 1871 French legislative election elects the first legislatu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
