ABSTRACT
Path functions and their basic properties are obtained by extending
the constructive theory of partition generating functions developed by
Sylvester, Durfee, Andrews and others. Path functions also arise when we
have an expansion of a function satisfying a linear difference equation.
We give infinite families of generalizations of the , . f
0
summation
formula and the q-analogs of Gauss' theorem and the limiting form of
Jackson's theorem. Our expansions provide an interesting trade-off
between complexity and rate of convergence. We add one free parameter to
the q-analog of the limiting form of Jackson's theorem and generalize this
result.
* Partially supported by NSF grant MCS78-07244A02.
1980AMS subjectclassifications(1985Revision).
Primary: 33A30, 05A15.
Secondary: 05A17, 11P57, 11P72, 39B40, 41A25.
Key words:
basic hypergeometric function, partition, generating function,
q-difference equation, rate of convergence, q-analog, binomial
theorem, Gauss' theorem, Jackson's theorem.
Library of Congress Cataloging-in-Publication Data
Kadell, Kevin W. J., 1950-
Path functions and generalized basic hypergeometric
functions.
(Memoirs of the American Mathematical Society,
ISSN 0065-9266; no. 360)
"Volume 65 number 360 (third of 5 numbers)."
Bibliography: p.
1. Functions, Hypergeometric. 2. Partitions (Mathematics)
3. Generating functions. I. Title. II. Series.
QA3.A57 no. 360 [QA353.H9] 510s [515'.55] 86-28866
ISBN 0-8218-2420-1
iv
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