Severin Wigert

	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'' (includin ..., including correctly describing its maximal order of growth. Wigert proved that :\limsup_\frac=\log2. Selected publications * * References * Swedish mathematicians 1871 births 1941 deaths {{Sweden-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Swedish People Swedes ( sv, svenskar) are a North Germanic ethnic group native to the Nordic region, primarily their nation state of Sweden, who share a common ancestry, culture, history and language. They mostly inhabit Sweden and the other Nordic countries, in particular Finland where they are an officially recognized minority, with a substantial diaspora in other countries, especially the 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, 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'' from the first century AD. The term is believed to have been derived from the Proto-Indo-European reflexive pronominal root, , as the Latin ''suus''. The word must have meant "one's own (tribesmen)". The same root and original meaning i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	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 Hypati ... [...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 mathemati ... [...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 Modular arithmetic, congruences and identity (mathematics), 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 summation, sum of the ''z''th Exponentiation, powers of the positive divisors of ''n''. It can be expressed in Summation#Capital ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Mathematical Proof A mathematical proof is an inferential argument for a 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 which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which 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 further mathematical work. Proofs employ logic expressed in mathematical symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Swedish Mathematicians Swedish or ' may refer to: Anything from or related to Sweden, a country in Northern Europe. Or, specifically: * Swedish language, a North Germanic language spoken primarily in Sweden and Finland ** Swedish alphabet, the official alphabet used by the Swedish language * Swedish people or Swedes, persons with a Swedish ancestral or ethnic identity A national or citizen of Sweden, see demographics of Sweden Culture of Sweden * Swedish cuisine See also * * Swedish Church (other) * Swedish Institute (other) * Swedish invasion (other) * Swedish Open (other) Swedish Open is a tennis tournament. Swedish Open may also refer to: Swedish Open (badminton) Swedish Open (table tennis) Swedish Open (squash) Swedish Open (darts) The Swedish Open is a darts tournament established in 1969, held in Malm� ... {{disambig Language and nationality disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	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, aside from Austria, 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. 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 – Giuseppe Garibaldi's group of French and Italian volunteer troops, in support of the French Third Republic, win a battle against the Prussians in the Battle of Dijon. * February 8 – 1871 French legislative election elect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]