Affiliation:
1. Wilfrid Laurier University, Waterloo, Canada
Abstract
Let K be a field of characteristic zero,
x
an independent variable,
E
the shift operator with respect to
x,
i.e.,
Ef
(
x
) =
f
(
x
+ 1) for an arbitrary
f
(
x
). Recall that a nonzero expression
F
(
x
) is called a hypergeometric term over K if there exists a rational function
r
(
x
) ∈ K(
x
) such that
F
(
x
+ 1)/
F
(
x
) =
r
(
x
). Usually
r
(
x
) is called the rational
certificate
of
F
(
x
). The problem of indefinite hypergeometric summation (anti-differencing) is: given a hypergeometric term
F
(
x
), find a hypergeometric term
G
(
x
) which satisfies the first order linear difference equation
(
E
− 1)
G
(
x
) =
F
(
x
). (1)
If found, write Σ
x
F
(
x
) =
G
(
x
) +
c
, where
c
is an arbitrary constant.
Publisher
Association for Computing Machinery (ACM)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献