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On summation of P-recursive sequences S. A. Abramov

Summary: On summation of P-recursive sequences
S. A. Abramov
Russian Academy of Sciences
Dorodnicyn Computing Centre
Vavilova 40, 119991, Moscow GSP-1, Russia
We consider sequences which satisfy a linear recurrence equation
Ly = 0 with polynomial coe cients. A criterion, i.e., a neces-
sary and su cient condition is proposed for validity of the discrete
Newton-Leibniz formula when a primitive (an inde nite sum) Rt of
a solution t of Ly = 0 is obtained either by Gosper's algorithm or
by the Accurate Summation algorithm (the operator R has rational-
function coe cients, ordR = ordL ; 1 in the Gosper case ordL = 1,
ordR = 0). Additionally we show that if Gosper's algorithm succeeds
on L, ordL = 1, then Ly = 0 always has some non-zero solutions
t, de ned everywhere, such that the discrete Newton-Leibniz formulaPw
k=v t(k) = u(w+1);u(v) is valid for u = Rt and any integer bounds
v w.
1 Introduction


Source: Abramov, Sergei A. - Dorodnicyn Computing Centre of the Russian Academy of Sciences


Collections: Mathematics; Computer Technologies and Information Sciences