Combinatorial proofs of Ramanujan's 11 summation and the q-Gauss summation
نویسنده
چکیده
Theorems in the theory of partitions are closely related to basic hypergeometric series. Some identities arising in basic hypergeometric series can be interpreted in the theory of partitions using Fpartitions. In this paper, Ramanujan’s 1ψ1 summation and the q-Gauss summation are established combinatorially.
منابع مشابه
q–GAUSS SUMMATION VIA RAMANUJAN AND COMBINATORICS
where |c/(ab)| < 1. Gauss’s name is attached to this theorem, because it is the qanalogue of Gauss’s summation for ordinary or Gaussian hypergeometric series. The theorem (1.1) was however first discovered by E. Heine [8] in 1847. We only know of two proofs of (1.1) up to recent times. The first proof, due to Heine [8], uses what we now call Heine’s transformation, and this proof can be found i...
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 105 شماره
صفحات -
تاریخ انتشار 2004