Hypergeometric functions | Q-analogs

Basic hypergeometric series

In mathematics, basic hypergeometric series, or q-hypergeometric series, are q-analogue generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series. A series xn is called hypergeometric if the ratio of successive terms xn+1/xn is a rational function of n. If the ratio of successive terms is a rational function of qn, then the series is called a basic hypergeometric series. The number q is called the base. The basic hypergeometric series was first considered by Eduard Heine. It becomes the hypergeometric series in the limit when base . (Wikipedia).

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Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 7

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Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 6

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Srinivasa Ramanujan | Barnes integral | Q-exponential | Rational function | Formal power series | Mathematics | Dixon's identity | G. N. Watson | Elliptic hypergeometric series | Rogers–Ramanujan identities | Eduard Heine | Q-analog | Bilateral hypergeometric series | Jacobi triple product