A representation theorem for ( q -)holonomic sequences
نویسندگان
چکیده
منابع مشابه
A representation theorem for (q-)holonomic sequences
Chomsky and Schützenberger showed in 1963 that the sequence dL(n), which counts the number of words of a given length n in a regular language L, satisfies a linear recurrence relation with constant coefficients for n, i.e., it is C-finite. It follows that every sequence s(n) which satisfies a linear recurrence relation with constant coefficients can be represented as dL1 (n)− dL2 (n) for two re...
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We describe a Mathematica package for dealing with q-holonomic sequences and power series. The package is intended as a q-analogue of the Maple package gfun and the Mathematica package GeneratingFunctions. It provides commands for addition, multiplication, and substitution of these objects, for converting between various representations (q-differential equations, q-recurrence equations, q-shift...
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In [Koepf (1992)] it was shown how for a given holonomic function a representation as a formal power series of hypergeometric type can be determined algorithmically. This algorithm – that we call FPS algorithm (Formal Power Series) – combines three steps to obtain the desired representation. The authors implemented this algorithm in the computer algebra system Maple as c̀onvert/FormalPowerSeries...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2014
ISSN: 0022-0000
DOI: 10.1016/j.jcss.2013.05.004