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normalized_fox-wright_function [2015/12/15 16:58] nikolaj |
normalized_fox-wright_function [2015/12/17 13:29] nikolaj |
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| ==== Function ==== | ==== Function ==== | ||
| | @#FF9944: definition | @#FF9944: $??$ | | | @#FF9944: definition | @#FF9944: $??$ | | ||
| - | | @#FF9944: definition | @#FF9944: ${}_p\Psi_q^*[\langle a_1, A_1\rangle,…,\langle a_p, A_p\rangle; \langle b_1, B_1\rangle,…,\langle a_q, A_q\rangle](z):= \sum_{n=0}^\infty c_n \dfrac{z^n}{n!}$ | | + | | @#FF9944: definition | @#FF9944: ${}_p\Psi_q^*[\langle a_1, A_1\rangle,…,\langle a_p, A_p\rangle; \langle b_1, B_1\rangle,…,\langle a_q, A_q\rangle](z):= \sum_{n=0}^\infty c_n z^n$ | |
| - | | @#BBDDEE: with | @#BBDDEE: $c_n = \dfrac{\prod_{m=1}^p \Gamma(a_m+A_m\cdot{n})\, /\, \Gamma(a_m)}{\prod_{j=1}^q \Gamma(b_j+B_m\cdot{n})\, /\, \Gamma(b_j)}$ | | + | | @#BBDDEE: with | @#BBDDEE: $c_n = \dfrac{1}{n!}\dfrac{\prod_{m=1}^p \Gamma(a_m+A_m\cdot{n})\, /\, \Gamma(a_m)}{\prod_{j=1}^q \Gamma(b_j+B_m\cdot{n})\, /\, \Gamma(b_j)}$ | |
| ----- | ----- | ||
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| === Subset of === | === Subset of === | ||
| [[Function]] | [[Function]] | ||
| + | === Related === | ||
| + | [[Generalized hypergeometric function]] | ||
