A Generalization of Gosper's Algorithm
نویسنده
چکیده
We present a derivation of Gosper's algorithm which permits generalization to higher-order recurrences with constant least and most signiicant coeecients. Like Gosper's algorithm, the generalized algorithm requires only "rational" operations (such as gcd and resultant computations) but no factorization.
منابع مشابه
A generalization of Gosper's algorithm
We present a derivation of Gosper's algorithm which permits generalization to higher-order recurrences with constant least and most significant coefficients. Like Gosper's algorithm, the generalized algorithm requires only 'rational' operations (such as gcd and resultant computations) but no factorization.
متن کاملA Generalization of Gosper's Algorithm to Bibasic Hypergeometric Summation
An algebraically motivated generalization of Gosper’s algorithm to indefinite bibasic hypergeometric summation is presented. In particular, it is shown how Paule’s concept of greatest factorial factorization of polynomials can be extended to the bibasic case. It turns out that most of the bibasic hypergeometric summation identities from literature can be proved and even found this way. A Mathem...
متن کاملOn the Gosper-Petkovs(ek representation of rational functions
We show that the uniqueness of the Gosper-Petkovšek representation of rational functions can be utilized to give a simpler version of Gosper’s algorithm. This approach also applies to Petkovšek’s generalization of Gosper’s algorithm, and its q-analogues by Abramov-Paule-Petkovšek and Böing-Koepf.
متن کاملA probabilistic model for the degree of the cancellation polynomial in Gosper's algorithm
Milenkovic and Compton in 2002 gave an analysis of the run time of Gosper’s algorithm applied to a random input. The main part of this was an asymptotic analysis of the random degree of the cancellation polynomial c(k) under various stipulated laws for the input. Their methods use probabilistic transform techniques. Here, a more general class of input distributions is considered, and limit laws...
متن کاملA Non-automatic (!) Application of Gosper’s Algorithm Evaluates a Determinant from Tiling Enumeration
1991 Mathematics Subject Classification. Primary 05A15; Secondary 05A16 05A17 05A19 05B45 33C20 52C20.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007