 
Summary: J. Symbolic Computation (1998) 11, 1000
Multibasic and Mixed Hypergeometric
GosperType Algorithms
ANDREJ BAUER y AND MARKO PETKOV Ÿ SEK z
y Department of Computer Science, Carnegie Mellon University, Pittsburgh PA, U.S.A.
z Department of Mathematics and Mechanics, University of Ljubljana, Slovenia
(Received 17 September 1997)
Gosper's summation algorithm finds a hypergeometric closed form of an indefinite sum
of hypergeometric terms, if such a closed form exists. We extend his algorithm to the
case when the terms are simultaneously hypergeometric and multibasic hypergeometric.
We also provide algorithms for finding polynomial as well as hypergeometric solutions
of recurrences in the mixed case. We do not require the bases to be transcendental, but
only that q
k 1
1
\Delta \Delta \Delta q
km
m 6= 1 unless k 1 = \Delta \Delta \Delta = km = 0. Finally, we generalize the concept
of greatest factorial factorization to the mixed hypergeometric case.
1. Introduction and notation
