A telescoping method for double summations

作者：Chen William Y C^*; Hou Qing Hu; Mu Yan Ping

来源：Journal of Computational and Applied Mathematics, 2006, 196(2): 553-566.

DOI：10.1016/j.cam.2005.10.010

• Zeilberger's algorithm
• double summation
• hypergeometric term

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 + (...) + ar(n)N-r and rational functions R-1 (n, i, j), R-2(n, i, j) such that LF = Delta (R1F) + Delta(j)(R2F). 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 upperbounds of the degrees and solving systems of linear equations. Our method is valid for the Andrews-Paule identity, Carlitz's identities, the Apery-Schmidt-Strehl identity, the Graham-Knuth-Patashnik identity, and the Petkovsek-Wilf-Zeilberger identity.

• 出版日期2006-11-15
• 单位南开大学