An improvement of the two-line algorithm for proving q-hypergeometric identities
نویسندگان
چکیده
منابع مشابه
A new elementary algorithm for proving q-hypergeometric identities
We give a fast elementary algorithm to get a small number n1 for an admissible q-properhypergeometric identity ∑ k F(n, k) = G(n), n ≥ n0 such that we can prove the identity by checking its correctness for n (n0 ≤ n ≤ n1). For example, we get n1 = 191 for the q-Vandermonde-Chu identity, n1 = 70 for a finite version of Jacobi’s triple product identity and n1 = 209 for an identity due to L.J. Rog...
متن کاملqMultiSum--a package for proving q-hypergeometric multiple summation identities
A Mathematica package for finding recurrences for q-hypergeometric multiple sums is introduced. Together with a detailed description of the theoretical background, we present several examples to illustrate its usage and range of applicability. In particular, various computer proofs of recently discovered identities are exhibited.
متن کاملAn algorithm for proving identities with Riordan transformations
The problem we consider in the present paper is how to find the closed form of a class of combinatorial sums, if it exists. The problem is well known in the literature, and is as old as Combinatorial Analysis is, since we can go back at least to Euler’s time. More recently, Riordan has tried to give a general approach to the subject, proposing a variety of methods, many of which are related to ...
متن کاملAn algorithmic proof theory for hypergeometric (ordinary and <Emphasis Type="Italic">q </Emphasis>) multisum/integral identities
It is shown that every 'proper-hypergeometric ' multisum/integral identity, or q-identity, with a fixed number of summations and/or integration signs, possesses a short, computer-constructible proof. We give a fast algorithm for finding such proofs. Most of the identities that involve the classical special functions of mathematical physics are readily reducible to the kind of identities treated...
متن کاملAn Algorithmic Proof Theory for Hypergeometric (ordinary and ``$q$'') Multisum/integral Identities
We now know ((Z1], WZ1]) that a large class of special function identities and binomial coeecient identities, are veriiable in a nite number of steps, since they can be embedded in the class of holonomic function identities, the elements of which are speciiable by a nite amount of data. Alas, the nite is usually a very big nite, and for most identities the holonomic approach Z1], that uses an e...
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: Discrete Mathematics
سال: 2003
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00686-6