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

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

Published electronically:
September 12, 2006

MathSciNet review:
2262846

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider sums of the form

**1.**L. Comtet,*Advanced Combinatorics*, D. Reidel, Dordrecht, 1974. MR**0460128 (57:124)****2.**R. P. Flowe, G. A. Harris, A note on generalized Vandermonde determinants, SIAM J. Matrix Anal. Appl.**14**(1993), no. 4, 1146-1151. MR**1238929 (94j:15005)****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*, Addison-Wesley, Reading, MA, 1969, Vol. 1, p. 84 (exercises 1.2.8.21 and 1.2.8.30), and p. 491, p. 492 (solutions). MR**0378456 (51:14624)****6.**Christian Krattenthaler, Advanced Determinant Calculus, Séminaire Lotharingien Combin.**42**(``The Andrews Festschrift'') (1999), Article B42q, 67 pp. MR**1701596 (2002i:05013)****7.**Marko Petkovšek, Herbert S. Wilf, and Doron Zeilberger, , A K Peters Ltd., Wellesley, MA, 1996. MR**1379802 (97j:05001)****8.**J. Riordan, Generating functions for powers of Fibonacci numbers, Duke. Math. J.**29**(1962), 5-12. MR**0132023 (24:A1870)****9.**David L. Russell, Sums of products of terms from linear recurrence sequences, Discrete Math**28**(1979), 65-79. MR**0542937 (82j:10021)****10.**Doron Zeilberger, A holonomic systems approach to special functions identities, J. Comput. Appl. Math.**32**(1990), no. 3, 321-368. MR**1090884 (92b:33014)**

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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:
https://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