Hypergeometric

Some articles on hypergeometric:

Appell Series
... In mathematics, Appell series are a set of four hypergeometric series F1, F2, F3, F4 of two variables that were introduced by Paul Appell (1880) and that generalize Gauss's hypergeometric ... formulas and expressions of these series in terms of hypergeometric series of one variable ...
Clausen's Formula
... (1828), expresses the square of a Gaussian hypergeometric series as a generalized hypergeometric series ... It states In particular it gives conditions for a hypergeometric series to be positive ...
Mary Celine Fasenmyer - Sister Celine's Method
... thesis concerning recurrence relations in hypergeometric series ... algorithmic method to find recurrence relations satisfied by sums of terms of a hypergeometric polynomial and requires only the series expansions of the ... The hypergeometric polynomials she studied are called Sister Celine's polynomials ...
Hypergeometric Differential Equation - History
... The term "hypergeometric series" was first used by John Wallis in his 1655 book Arithmetica Infinitorum ... Hypergeometric series were studied by Leonhard Euler, but the first full systematic treatment was given by Carl Friedrich Gauss (1813) ... characterisation by Bernhard Riemann of the hypergeometric function by means of the differential equation it satisfies ...
Hypergeometric Differential Equation
... In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,bcz) is a special function represented by the hypergeometric series, that includes many ...