A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities
نویسندگان
چکیده
منابع مشابه
A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities
Gosper’s algorithm for indefinite hypergeometric summation, see e.g. Gosper (1978) or Lafon (1983) or Graham, Knuth and Patashnik (1989), belongs to the standard methods implemented in most computer algebra systems. Exceptions are, for instance, the 2.xVersions of the Mathematica system where symbolic summation is done by different means. A brief discussion is given in section 5. Current intere...
متن کاملDiscovering and Proving Infinite Binomial Sums Identities
We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of π or log(2). In order to perform these simplifications, we view the series as specializations of generating series. For these generating series, we derive integral representations in terms of root-valued iterated integrals. Using substitutions, we express the inter...
متن کامل87. Binomial Coefficient Identities and Hypergeometric Series
In recent months I have come across many instances in which someone has found what they believe is a new result, in which they evaluate in closed form a sum involving binomial coefficients or factorials. In each case they have managed to do that either by using the recent powerful method of Wilf and Zeilberger (the W–Z method) [6], or by comparing coefficients in some ad hoc algebraic identity....
متن کاملA q-analogue of Zhang's binomial coefficient identities
In this paper, we prove some identities for the alternating sums of squares and cubes of the partial sum of the q-binomial coefficients. Our proof also leads to a q-analogue of the sum of the first n squares due to Schlosser.
متن کاملCombinatorial proofs of a kind of binomial and q-binomial coefficient identities
We give combinatorial proofs of some binomial and q-binomial identities in the literature, such as ∞ ∑ k=−∞ (−1)kq(9k2+3k)/2 [ 2n n + 3k ] = (1 + q) n−1 ∏ k=1 (1 + q + q) (n ≥ 1),
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1995
ISSN: 0747-7171
DOI: 10.1006/jsco.1995.1071