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hypergeometric series

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  • Hypergeometric series — In mathematics, a hypergeometric series is a power series in which the ratios of successive coefficients k is a rational function of k . The series, if convergent, will define a hypergeometric function which may then be defined over a wider… …   Wikipedia

  • hypergeometric series — noun Any power series such that the ratio of the (k+1) th and the k th terms is a rational function of the natural integer k. See Also: hypergeometric function, hypergeometric equation, confluent hypergeometric series, basic hypergeometric series …   Wiktionary

  • hypergeometric series — hipergeometrinė eilutė statusas T sritis fizika atitikmenys: angl. hypergeometric series vok. hypergeometrische Reihe, f rus. гипергеометрический ряд, m pranc. série hypergéométrique, f …   Fizikos terminų žodynas

  • Basic hypergeometric series — In mathematics, the basic hypergeometric series, also sometimes called the hypergeometric q series, are q analog generalizations of ordinary hypergeometric series. Two basic series are commonly defined, the unilateral basic hypergeometric series …   Wikipedia

  • Elliptic hypergeometric series — In mathematics, an elliptic hypergeometric series is a series Σcn such that the ratio cn/cn−1 is an elliptic function of n, analogous to generalized hypergeometric series where the ratio is a rational function of n, and basic hypergeometric… …   Wikipedia

  • Bilateral hypergeometric series — In mathematics, a bilateral hypergeometric series is a series Σan summed over all integers n, and such that the ratio an/an+1 of two terms is a rational function of n. The definition of the generalized hypergeometric series is similar, except… …   Wikipedia

  • Lauricella hypergeometric series — In 1893 G. Lauricella defined and studied four hypergeometric series of three variables. They are::F A^{(3)}(a,b 1,b 2,b 3,c 1,c 2,c 3;x 1,x 2,x 3) = sum {i 1,i 2,i 3=0}^{infty} frac{(a) {i 1+i 2+i 3} (b 1) {i 1} (b 2) {i 2} (b 3) {i 3 {(c 1) {i… …   Wikipedia

  • Hypergeometric — can refer to various related mathematical topics:*Hypergeometric series, p F q , a power series **Confluent hypergeometric function, 1 F 1, also known as the Kummer function **Euler hypergeometric integral, an integral representation of 2 F 1… …   Wikipedia

  • Hypergeometric identities — In mathematics, hypergeometric identities are equalities involving sums over hypergeometric terms, i.e. the coefficients occurring in hypergeometric series. These identities occur frequently in solutions to combinatorial problems, and also in the …   Wikipedia

  • Hypergeometric differential equation — In mathematics, the hypergeometric differential equation is a second order linear ordinary differential equation (ODE) whose solutions are given by the classical hypergeometric series. Every second order linear ODE with three regular singular… …   Wikipedia

  • Hypergeometric function of a matrix argument — In mathematics, the hypergeometric function of a matrix argument is a generalization of the classical hypergeometric series. It is the closed form expression of certain multivariate integrals, especially ones appearing in random matrix theory.… …   Wikipedia


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