The multi-variate analogue of telescoping is a challenging problem, with the Andrews-Paule identity as a benchmark example. We shall discuss various approaches to the multi-variate …

Telescoping Series Definition A telescoping series has internal cancellation of terms in its partial sums. Basic Forms of Telescoping Series (f is a function): P [f(k + 1) f(k)]

Lecture 17: Series (II) Telescoping Series A telescoping series is a special type of series for which many terms cancel in the nth partial sums. te out the nth partial sums of the series. And if the …

Based on Gosper's algorithm, we present an approach to the tele-scoping of general sequences. Along this approach, we propose a summation formula and a bibasic extension of Ma's …

What is a telescoping series? Brie y, a telescoping series is a sum that is characterized by partial sums (called telescoping sums) that contain pairs of consecutive terms which cancel each …

3. The Heart of Telescoping A telescoping expression is nothing but a long sequence of tiny cancellings. The hard part is recognizing the pattern that lets us start canceling. So our first big …

In the present paper this fast algorithm is described in much more detail and several applications to combinatorics, probability, computation, logic and orthogonal poly- nomials are given. A …