A Telescoping method for Double Summations
| dc.creator | Chen, William Y. C. | |
| dc.creator | Hou, Qing-Hu | |
| dc.creator | Mu, Yan-Ping | |
| dc.date | 2005-04-26 | |
| dc.date | 2005-11-02 | |
| dc.date.accessioned | 2026-07-07T06:39:50Z | |
| dc.date.available | 2026-07-07T06:39:50Z | |
| dc.description | We present a method to prove hypergeometric double summation identities. Given a hypergeometric term $F(n,i,j)$, we aim to find a difference operator $ L=a_0(n) N^0 + a_1(n) N^1 +...+a_r(n) N^r $ and rational functions $R_1(n,i,j),R_2(n,i,j)$ such that $ L F = Δ_i (R_1 F) + Δ_j (R_2 F)$. Based on simple divisibility considerations, we show that the denominators of $R_1$ and $R_2$ must possess certain factors which can be computed from $F(n, i,j)$. Using these factors as estimates, we may find the numerators of $R_1$ and $R_2$ by guessing the upper bounds of the degrees and solving systems of linear equations. Our method is valid for the Andrews-Paule identity, Carlitz's identities, the Apéry-Schmidt-Strehl identity, the Graham-Knuth-Patashnik identity, and the Petkovšek-Wilf-Zeilberger identity. | |
| dc.description | 22 pages. to appear in J. Computational and Applied Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0504525 | |
| dc.identifier | http://arxiv.org/abs/math/0504525 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101229 | |
| dc.subject | Combinatorics | |
| dc.subject | 33F10, 68W30 | |
| dc.title | A Telescoping method for Double Summations | |
| dc.type | text |