|
Severin Wigert
Carl Severin Wigert (1871–1941) was a Swedish mathematician who created 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\l ... and worked on the divisor function, 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] |
Swedish People
Swedes ( sv, svenskar) are a North Germanic peoples, 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, Swedish-speaking population of Finland, in particular Finland where they are an officially recognized minority, with a substantial Swedish diaspora, diaspora in other countries, Swedish Americans, 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 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 to have been derived from the Proto-Indo-European language ... [...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 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 Pythagoreans, 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 mathemat ... [...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 for "''d'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is an Inference, inferential 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 which establish logical certainty, to be distinguished from empirical evidence, 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 furthe ... [...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 The demography of Sweden is monitored by the ''Statistiska centralbyrån'' (Statistics Sweden). Sweden's population was 10,481,937 (May 2022), making it the 15th-most populous country in Europe after Czech Republic, the 10th-most populous m ... ** Culture of Sweden * Swedish cuisine See also * * Swedish Church (other) * Swedish Institute (other) * Swedish invasion (other) * Swedish Open (other) {{disambig Language and nationality disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1871 Births
Events January–March * January 3 Events Pre-1600 * 69 – The Roman legions on the Rhine refuse to declare their allegiance to Galba, instead proclaiming their legate, Aulus Vitellius, as emperor. * 250 – Emperor Decius orders everyone in the Roman Empire (except ... – 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 (1871), 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 employm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
_(LOC)_-_Flickr_-_The_Library_of_Congress.jpg "Click for more on -> 1871 Births")