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[50] puter programs for simplifying sums
that involve binomial coe
cients.
Exercise in
The Art puter Programming, Volume 1: Fundamental Algorithms
by Donald E. Knuth,
Addison Wesley, Reading, Massachusetts, 1968.
A=B
Marko Petkov
sek Herbert S. Wilf
University of Ljubljana University of Pennsylvania
Ljubljana, Slovenia Philadelphia, PA, USA
Doron Zeilberger
Temple University
Philadelphia, PA, USA
April 27, 1997
ii
Contents
Foreword vii
AQuickStart... ix
I Background 1
1 Proof Machines 3
.............. 3
....................... 7
........................... 8
?............................ 9
......................... 11
............................ 12
...................... 12
Elliptic function identities ........................ 13
2 Tightening the Target 17
................................ 17
.................................. 21
;anexample................ 23
.......................... 27
.............................. 29
.................. 30
.................................. 31
3 The Hypergeometric Database 33
................................ 33
........................... 34
............... 35
eshypergeometricseries.............. 39
iv CONTENTS
.............. 42
............................ 44
?............... 48
.................................. 50
II The Five Basic Algorithms 53
4 Sister Celine’s Method 55
...........