List of hypergeometric identities information

function lists identities for more general hypergeometric functions Bailey's list is a list of the hypergeometric function identities in Bailey (1935)...

different series of identities. The theory of the algorithmic discovery of identities remains an active research topic. The term "hypergeometric series" was...

identities Hypergeometric function identities List of integrals of logarithmic functions List of topics related to π List of trigonometric identities...

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...

theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k {\displaystyle k} successes...

Kazuhiko Aomoto: Aomoto–Gel'fand hypergeometric function - Aomoto integral Paul Émile Appell (1855–1930): Appell hypergeometric series, Appell polynomial, Generalized...

coefficient Gould's sequence Hyperfactorial Hypergeometric distribution Hypergeometric function identities Hypergeometric series Incomplete beta function Incomplete...

x^{\overline {n}}} are increasingly popular. In the theory of special functions (in particular the hypergeometric function) and in the standard reference work Abramowitz...

the convergence of an alternating series and is also frequently applied to the hypergeometric series Euler rotation equations, a set of first-order ODEs...

Board of Governors Professor of Mathematics at Rutgers University. Zeilberger has made contributions to combinatorics, hypergeometric identities, and q-series...

hypergeometric functions Gauss's criterion – described on Encyclopedia of Mathematics Gauss's hypergeometric theorem, an identity on hypergeometric series...

hypergeometric functions, and who found many generalizations of the Rogers–Ramanujan identities. Slater was born in 1922 and homeschooled for much of...

obtained in terms of the generalized hypergeometric function. Let Δ ( k , − n ) {\displaystyle \Delta (k,-n)} denote the array of k {\displaystyle k}...

discussed elliptic integrals, hypergeometric series, and his theory of divergent series, which Rao said ultimately convinced him of Ramanujan's brilliance....

. The hypergeometric function is an example of a four-argument function. The number of arguments that a function takes is called the arity of the function...

basic hypergeometric series. He introduced the Mehler–Heine formula. Heinrich Eduard Heine was born on 16 March 1821 in Berlin, as the eighth child of banker...

curves, fractal dimension, hypergeometric functions, Fibonacci polytopes, geometry, graph theory, music, and art. Biography of Verner Emil Hoggatt Jr. by...

Laguerre polynomials may be defined in terms of hypergeometric functions, specifically the confluent hypergeometric functions, as L n ( α ) ( x ) = ( n + α...

numbers. Such characteristic-zero identities follow generally from one of many possible identities on the hypergeometric series. Weisstein, Eric W. "Legendre...

Eulerian number Hypergeometric function List of factorial and binomial topics Macaulay representation of an integer Motzkin number Multiplicities of entries in...

analogue of Gaussian binomial coefficients". Fibonacci Quarterly. 12: 129–132. MR 0354537. Andrews, George E. (1974). "Applications of basic hypergeometric functions"...

closely related to hypergeometric series. In the form of spherical harmonics, they express the symmetry of the two-sphere under the action of the Lie group...