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The Extended Zeilberger Algorithm with Parameters
Zeilberger's algorithm the extended Zeilberger algorithm the Gosper algorithm hypergeometric series orthogonal polynomials
2014/6/3
Two hypergeometric terms f(k) and g(k) are said to be similar if the ratio f(k) =g(k) is a rational function of k. For similar hypergeometric terms f1(k),..., fm(k), we present an algorithm, called th...
The Abel-Zeilberger Algorithm
Abel's lemma Zeilberger's algorithm holonomic sequence linear difference equation
2014/6/3
By combining Abel’s lemma on summation by parts with Zeilberger’s algorithm, we give an algorithm, called the Abel-Zeilberger algorithm, to find recurrence relations for definite summation...
Nonterminating Basic Hypergeometric Series and the q-Zeilberger Algorithm
basic hypergeometric series q-Zeilberger algorithm Bailey's very-well-poised summation formula Sears-Carlitz transformation Rogers-Fine identity
2014/6/3
We present a systematic method for proving nonterminating basic hypergeometric identities. Assume that k is the summation index. By setting a parameter x to xqn, we may find a recurrence relation of t...