Closed form summation of -finite sequences

Authors:
Curtis Greene and Herbert S. Wilf

Journal:
Trans. Amer. Math. Soc. **359** (2007), 1161-1189

MSC (2000):
Primary 05A15, 05A19; Secondary 11B37, 11B39

Published electronically:
September 12, 2006

MathSciNet review:
2262846

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider sums of the form

**1.**Louis Comtet,*Advanced combinatorics*, Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht, 1974. The art of finite and infinite expansions. MR**0460128****2.**Randolph P. Flowe and Gary A. Harris,*A note on generalized Vandermonde determinants*, SIAM J. Matrix Anal. Appl.**14**(1993), no. 4, 1146–1151. MR**1238929**, 10.1137/0614079**3.**Charles Jordan,*Calculus of Finite Differences*, Chelsea, New York, 1950.**4.**Curtis Greene, Herbert S. Wilf,`CFSum.nb`, (Mathematica notebook),`<http://www.haverford.edu/math/cgreene/cfsum.nb>`,`<http://www.math.upenn.edu/``wilf/website/cfsum.nb>`.**5.**Donald E. Knuth,*The art of computer programming*, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. Volume 1: Fundamental algorithms; Addison-Wesley Series in Computer Science and Information Processing. MR**0378456****6.**C. Krattenthaler,*Advanced determinant calculus*, Sém. Lothar. Combin.**42**(1999), Art. B42q, 67 pp. (electronic). The Andrews Festschrift (Maratea, 1998). MR**1701596****7.**Marko Petkovšek, Herbert S. Wilf, and Doron Zeilberger,*𝐴=𝐵*, A K Peters, Ltd., Wellesley, MA, 1996. With a foreword by Donald E. Knuth; With a separately available computer disk. MR**1379802****8.**John Riordan,*Generating functions for powers of Fibonacci numbers*, Duke Math. J.**29**(1962), 5–12. MR**0132023****9.**David L. Russell,*Sums of products of terms from linear recurrence sequences*, Discrete Math.**28**(1979), no. 1, 65–79. MR**542937**, 10.1016/0012-365X(79)90186-9**10.**Doron Zeilberger,*A holonomic systems approach to special functions identities*, J. Comput. Appl. Math.**32**(1990), no. 3, 321–368. MR**1090884**, 10.1016/0377-0427(90)90042-X

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Additional Information

**Curtis Greene**

Affiliation:
Department of Mathematics, Haverford College, Haverford, Pennsylvania 19041-1392

Email:
cgreene@haverford.edu

**Herbert S. Wilf**

Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395

Email:
wilf@math.upenn.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-06-03994-8

Keywords:
Summation,
closed form,
$C$-finite,
recurrences

Received by editor(s):
May 20, 2004

Received by editor(s) in revised form:
December 9, 2004

Published electronically:
September 12, 2006

Dedicated:
To David Robbins

Article copyright:
© Copyright 2006
American Mathematical Society