)其中p 为自然数,g (n ,k )=R (n ,k )F (n ,k ).可利用m a p l e 软件包h s u m 15.m p l (可以从h t t p :ʊw w w.m a t h e m a t i k .u n i -k a s s e l .d e /~k o e p f /h s u m 15.m p l 下载)求得R (n ,k ),c 0(n ),c...
QDifferenceEquations Zeilberger perform Zeilberger's algorithm (q-difference case) Calling Sequence Parameters Description Examples References Calling Sequence Zeilberger( T , n , k , q , Qn ) Parameters T - q-hypergeometric term in and n - name k -...
A terminating condition of the well-known Zeilberger's algorithm for a given hypergeometric term T( n, k) is presented. It is shown that the only information on T( n, k) that one needs in order to determine in advance whether this algorithm will succeed is the rational function T( n,...
algorithm. Weshow that,thehypergeometric function 2Fl(a,b;c;x)is the onlypower series solutiontotheEuler’S hypergeometric equation atx=0withvalue 1atX=0.Given arational function妒@)and aradical function O(x)with parameters,we caninduce ...
Zeilberger’s fast algorithm exploits a specialized version of Gosper’s algorithm for the indefinite summation problem; i.e. given a hypergeometric sequence t(k), the problem of finding another sequence T (k) such that t(k) = ∆k T (k) = T (k + 1) − T (k). The ...
perform Koepf-Zeilberger's algorithm Calling Sequence Parameters Description Examples References Calling Sequence KoepfZeilberger(T, n, k, En) Parameters T - (m, l)-fold hypergeometric term in n and k n - name k - name En - name; denote the shift operator with respect to ...
S.A. Abramov, Applicability of Zeilberger's algorithm to hypergeometric terms, In: Proc. Int. Symp. on Symbolic and Algebraic Computation, ACM Press, 2002.Applicability of Zeilberger’s algorithm to hypergeometric terms - Abramov, A - 2002 () Citation Context ...lberger’s algorithm (see ...
DEtools Zeilberger perform Zeilberger's algorithm (differential case) Calling Sequence Parameters Description Examples References Calling Sequence Zeilberger( F , x , y , Dx ) Zeilberger( F , x , y , Dx , 'gosper_free') Parameters F - hyperexponential...
In this chapter, we introduce Zeilberger's extension of Gosper's algorithm, using which one can not only prove hypergeometric identities but also sum definite series in many cases, if they represent hypergeometric terms.Wolfram KoepfUniversität KasselKoornwinder, T.H.: On Zeilberger’s algorithm...
It is shown how the performance of Zeilberger's algorithm and its q -version for proving ( q -)hypergeometric summation identities can be dramatically improved by a frequently missed optimization on the programming level and by applying certain kinds of substitutions to the summand. These methods...