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Kampé De Fériet Function
In mathematics, the Kampé de Fériet function is a two-variable generalization of the generalized hypergeometric series, introduced by Joseph Kampé de Fériet Marie-Joseph Kampé de Fériet (Paris, 14 May 1893 – Villeneuve d'Ascq, 6 April 1982) was professor at Université Lille Nord de France from 1919 to 1969. Besides his works on mathematics and fluid mechanics, he directed the ''Institut de mé .... The Kampé de Fériet function is given by : ^F_\left( \begin a_1,\cdots,a_p\colon b_1,b_1';\cdots;b_q,b_q'; \\ c_1,\cdots,c_r\colon d_1,d_1';\cdots;d_s,d_s'; \end x,y\right)= \sum_^\infty\sum_^\infty\frac\frac\cdot\frac. Applications The general sextic equation can be solved in terms of Kampé de Fériet functions. References * * * External links * Hypergeometric functions {{analysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Hypergeometric Function
In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by ''n'' is a rational function of ''n''. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic continuation. The generalized hypergeometric series is sometimes just called the hypergeometric series, though this term also sometimes just refers to the Gaussian hypergeometric series. Generalized hypergeometric functions include the (Gaussian) hypergeometric function and the confluent hypergeometric function as special cases, which in turn have many particular special functions as special cases, such as elementary functions, Bessel functions, and the classical orthogonal polynomials. Notation A hypergeometric series is formally defined as a power series :\beta_0 + \beta_1 z + \beta_2 z^2 + \dots = \sum_ \beta_n z^n in which the ratio of successive coefficients is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Kampé De Fériet
Marie-Joseph Kampé de Fériet (Paris, 14 May 1893 – Villeneuve d'Ascq, 6 April 1982) was professor at Université Lille Nord de France from 1919 to 1969. Besides his works on mathematics and fluid mechanics, he directed the ''Institut de mécanique des fluides de Lille'' ( ONERA Lille) and taught fluid dynamics and information theory at École centrale de Lille from 1930 to 1969. He devised the Kampé de Fériet functions, which further generalize the generalized hypergeometric function In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by ''n'' is a rational function of ''n''. The series, if convergent, defines a generalized hypergeometric function, which ...s. He was an Invited Speaker of the ICM in 1928 at Bologna, in 1932 at Zurich, and in 1954 at Amsterdam. Works * J. Kampé de Fériet & P.E. Appell ''Fonctions hypergéometriques et hypersphériques'' (Paris, Gauthier-Villars, 1926) * J. K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sextic Equation
In algebra, a sextic (or hexic) polynomial is a polynomial of degree six. A sextic equation is a polynomial equation of degree six—that is, an equation whose left hand side is a sextic polynomial and whose right hand side is zero. More precisely, it has the form: :ax^6+bx^5+cx^4+dx^3+ex^2+fx+g=0,\, where and the ''coefficients'' may be integers, rational numbers, real numbers, complex numbers or, more generally, members of any field. A sextic function is a function defined by a sextic polynomial. Because they have an even degree, sextic functions appear similar to quartic functions when graphed, except they may possess an additional local maximum and local minimum each. The derivative of a sextic function is a quintic function. Since a sextic function is defined by a polynomial with even degree, it has the same infinite limit when the argument goes to positive or negative infinity. If the leading coefficient is positive, then the function increases to positive infinity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
