U. B. Singh, Some summation formula for multibasic hypergeometric series, Glasnik Mat. 31(51) (1996) 263--268. Home/Search Document Not in Database Summary Related Articles Check |
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Multibasic and Mixed Hypergeometric Gosper-Type Algorithms - Bauer, Petkovsek (Correct)
....this section by giving some examples of sums which can be evaluated automatically by MixedGosper. We write (a; q)n = Q n Gamma1 i=0 (1 Gamma aq ) Many bibasic examples can be found in [7] and [20] An indefinite multibasic summation formula (too big to reproduce it here) is proved in [21]. The formula contains an arbitrary number, k, of bases. Such formulae cannot be proved by our algorithm. However, any specialization of this formula in which k is replaced by a specific natural number can be, at least in principle, not only proved, but also derived by MixedGosper. In [21] it is ....
....in [21] The formula contains an arbitrary number, k, of bases. Such formulae cannot be proved by our algorithm. However, any specialization of this formula in which k is replaced by a specific natural number can be, at least in principle, not only proved, but also derived by MixedGosper. In [21], it is shown that several well known basic and bibasic summation formulae can be obtained as specializations of this k basic master formula. The following two examples are due to Gosper [10] Example 6.1 In this tribasic example F = Q (a; b; c; p; q; r) where a; b; c are parameters and p; q; r ....
U. B. Singh, Some summation formula for multibasic hypergeometric series, Glasnik Mat. 31(51) (1996) 263--268.
Multibasic and Mixed Gosper's Algorithm - Bauer, Petkovsek (Correct)
....= x= 1 Gamma qy(x 1) and we find that Sn 1 Gamma Sn = tn is satisfied by Sn = n(q; q)n C. Here C is an additive constant which, for our initial sum, equals S0 = 0. Example 6. 2 For a multibasic example, we refer to the indefinite summation formula (too big to be reproduced here) proved in [14]. The formula contains an arbitrary number, k, of bases. Such formulae cannot be proved by our algorithm. However, any specialization of this formula in which k is replaced by a specific natural number (such as 2 or 113) can be, at least in principle, not only proved, but also derived by ....
....formula contains an arbitrary number, k, of bases. Such formulae cannot be proved by our algorithm. However, any specialization of this formula in which k is replaced by a specific natural number (such as 2 or 113) can be, at least in principle, not only proved, but also derived by m m Gosper. In [14], it is shown that several known basic and bibasic summation formulae can be obtained as specializations of this k basic master formula. 7 Concluding remarks We have shown how to compute the hypergeometric canonical form of rational functions, how to find polynomial solutions of recurrences, and ....
U. B. Singh, Some summation formula for multibasic hypergeometric series, Glasnik Mat. 31(51) (1996) 263--268.
Multibasic and Mixed Hypergeometric Gosper-Type Algorithms - Bauer, Petkovsek (Correct)
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J. Comb. 3, #R19. Singh, U. B. (1996). Some summation formula for multibasic hypergeometric series. Glasnik Mat. 31(51), 263--268.
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