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September 27, 2008

Bibliography

1
S. A. Abramov, P. Paule, and M. Petkovšek.
$q$-Hypergeometric solutions of $q$-difference equations.
Discrete Math., 180:3-22, 1998.
2
H. Alzer, S. Gerhold, M. Kauers, and A. Lupas.
On Turan's inequality for Legendre polynomials.
Expositiones Mathematicae, 25(2):181-186, May 2007.
3
G. E. Andrews, A. Knopfmacher, and P. Paule.
An infinite family of Engel expansions of Rogers-Ramanujan type.
Adv. in Appl. Math., 25:2-11, 2000.
4
G. E. Andrews, A. Knopfmacher, P. Paule, and H. Prodinger.
$q$-Engel series expansions and Slater's identities.
Quaestiones Math., 24:1-14, 2001.
5
G. E. Andrews and P. Paule.
MacMahon's partition analysis IV: Hypergeometric multisums.
Sém. Lothar. Combin., B42i:1-24, 1999.
6
G. E. Andrews and P. Paule.
Macmahon's partition analysis XI: Broken diamonds and modular forms.
Acta Arith., 126:281-294, 2007.
7
G. E. Andrews, P. Paule, and A. Riese.
MacMahon's partition analysis III: The Omega package.
European J. Combin., 22:887-904, 2001.
8
G. E. Andrews, P. Paule, and A. Riese.
MacMahon's partition analysis IX: $k$-Gon partitions.
Bull. Austral. Math. Soc., 64:321-329, 2001.
9
G. E. Andrews, P. Paule, and A. Riese.
MacMahon's partition analysis VI: A new reduction algorithm.
Ann. Comb., 5:251-270, 2001.
10
G. E. Andrews, P. Paule, and A. Riese.
MacMahon's partition analysis VIII: Plane partition diamonds.
Adv. in Appl. Math., 27:231-242, 2001.
11
G. E. Andrews, P. Paule, and C. Schneider.
Plane partitions VI: Stembridge's TSPP theorem.
Advances in Applied Math. Special Issue Dedicated to Dr. David P. Robbins. Edited by D. Bressoud, 34(4):709-739, 2005.
12
A. Becirovic, P. Paule, V. Pillwein, A. Riese, C. Schneider, and J. Schöberl.
Hypergeometric summation algorithms for high order finite elements.
Computing, 78(3):235-249, 2006.
13
J. P. Bell and S. Gerhold.
On the positivity set of a linear recurrence sequence.
Israel J. Math., 157:333-345, 2007.
14
J. P. Bell, S. Gerhold, M. Klazar, and F. Luca.
Non-holonomicity of sequences defined via elementary functions.
Annals of Combinatorics, 2007.
To appear.
15
A. Berkovich and P. Paule.
Lattice paths, $q$-multinomials and two variants of the Andrews-Gordon identities.
Ramanujan J., 5:409-424, 2001.
16
A. Berkovich and P. Paule.
Variants of the Andrews-Gordon identities.
Ramanujan J., 5:391-404, 2001.
17
A. Berkovich and A. Riese.
A computer proof of a polynomial identity implying a partition theorem of Göllnitz.
Adv. in Appl. Math., 28:1-16, 2002.
18
F. Caruso.
A Macsyma implementation of Zeilberger's fast algorithm.
Sém. Lothar. Combin., S43c:1-8, 1999.
19
F. Chyzak, I. Gutman, and P. Paule.
Predicting the number of hexagonal systems with 24 and 25 hexagons.
MATCH, 40:139-151, 1999.
20
F. Chyzak, P. Paule, O. Scherzer, A. Schoisswohl, and B. Zimmermann.
The construction of orthonormal wavelets using symbolic methods and a matrix analytical approach for wavelets on the interval.
Experiment. Math., 10:67-86, 2001.
21
K. Driver, H. Prodinger, C. Schneider, and A. Weideman.
Padé Approximations to the Logarithm II: Identities, Recurrences, and Symbolic Computation.
Ramanujan Journal, 11(2):139-158, April 2006.
22
K. Driver, H. Prodinger, C. Schneider, and A. Weideman.
Padé Approximations to the Logarithm III: Alternative Methods and Additional Results.
Ramanujan Journal, 12(3):299-314, 2006.
23
P. Flajolet, S. Gerhold, and B. Salvy.
On the non-holonomic character of logarithms, powers and the nth prime function.
Electronic Journal of Combinatorics, 11(2):1-16, 2005.
24
S. Gerhold.
On some non-holonomic sequences.
Electronic Journal of Combinatorics, 11(1):1-8, 12 2004.
25
S. Gerhold.
Point Lattices and Oscillating Recurrence Sequences.
Journal of Difference Equations and Applications, 11(6):515-533, 2005.
26
S. Gerhold, L. Glebsky, C. Schneider, H. Weiss, and B. Zimmermann.
Limit states for one-dimensional schelling segregation models.
Communications in Nonlinear Science and Numerical Simulations, 2007.
To appear.
27
S. Gerhold and M. Kauers.
A computer proof of Turan's inequality.
Journal of Inequalities in Pure and Applied Mathematics, 7(2):1-4, May 2006.
Article 42.
28
I. Gutman and P. Paule.
The variance of the vertex degrees of randomly generated graphs.
Publ. Fac. Electr. Engrg. Ser. Mat., 13:30-35, 2002.
29
M. Kauers.
Shift equivalence of p-finite sequences.
The Electronic Journal of Combinatorics, 13(1):1-16, 2006.
R100.
30
M. Kauers.
SumCracker--A package for manipulating symbolic sums and related objects.
Journal of Symbolic Computation, 41(9):1039-1057, 2006.
31
M. Kauers.
An algorithm for deciding zero equivalence of nested polynomially recurrent sequences.
Transactions on Algorithms, 3(2):1-13, 2007.
article 18.
32
M. Kauers and P. Paule.
A computer proof of Moll's log-concavity conjecture.
Proceedings of the AMS, 135(12):3847-3856, 2007.
33
M. Kauers and C. Schneider.
Indefinite summation with unspecified summands.
Discrete Math., 306(17):2073-2083, 2006.
34
C. Koutschan.
Regular languages and their generating functions: The inverse problem.
Theoretical Computer Science, pages 1-10, 2007.
To appear.
35
P. J. Larcombe, A. Riese, and B. Zimmermann.
Computer proofs of matrix product identities.
J. Algebra Appl., 3:105-109, 2004.
36
R. Lyons, P. Paule, and A. Riese.
A computer proof of a series evaluation in terms of harmonic numbers.
Appl. Algebra Engrg. Comm. Comput., 13:327-333, 2002.
37
P. Paule, V. Pillwein, C. Schneider, and S. Schöberl.
Hypergeometric Summation Techniques for High Order Finite Elements.
PAMM, 6, 2006.
38
P. Paule and H. Prodinger.
Fountains, histograms, and $q$-identities.
Discrete Math. Theor. Comput. Sci., 6:101-106, 2003.
39
P. Paule and C. Schneider.
Computer proofs of a new family of harmonic number identities.
Adv. in Appl. Math., 31(2):359-378, 2003.
40
P. Paule and C. Schneider.
Truncating binomial series with symbolic summation.
INTEGERS. Electronic Journal of Combinatorial Number Theory, 7:1-9, 2007.
41
A. Riese.
qMultiSum -- A package for proving $q$-hypergeometric multiple summation identities.
J. Symbolic Comput., 35:349-376, 2003.
42
C. Schneider.
An implementation of Karr's summation algorithm in Mathematica.
Sém. Lothar. Combin., S43b:1-10, 2000.
43
C. Schneider.
A collection of denominator bounds to solve parameterized linear difference equations in ${\Pi}{\Sigma}$-extensions.
An. Univ. Timisoara Ser. Mat.-Inform., 42(2):163-179, 2004.
Extended version of Proc. SYNASC'04; preliminary version online.
44
C. Schneider.
The summation package Sigma: Underlying principles and a rhombus tiling application.
Discrete Math. Theor. Comput. Sci., 6(2):365-386, 2004.
45
C. Schneider.
Degree bounds to find polynomial solutions of parameterized linear difference equations in ${\Pi}{\Sigma}$-fields.
Appl. Algebra Engrg. Comm. Comput., 16(1):1-32, 2005.
46
C. Schneider.
A new Sigma approach to multi-summation.
Advances in Applied Math. Special Issue Dedicated to Dr. David P. Robbins. Edited by D. Bressoud, 34(4):740-767, 2005.
47
C. Schneider.
Product representations in ${\Pi}{\Sigma}$-fields.
Annals of Combinatorics, 9(1):75-99, 2005.
48
C. Schneider.
Solving parameterized linear difference equations in terms of indefinite nested sums and products.
J. Differ. Equations Appl., 11(9):799-821, 2005.
49
C. Schneider.
Apéry's double sum is plain sailing indeed.
Electron. J. Combin., 14:1-3, 2007.
N5.
50
C. Schneider.
Simplifying sums in ${\Pi}{\Sigma}$-extensions.
J. Algebra Appl., 6(3):415-441, 2007.
51
C. Schneider.
Symbolic summation assists combinatorics.
Sem. Lothar. Combin., 56:1-36, 2007.
Article B56b.
52
C. Schneider and R. Pemantle.
When is 0.999... equal to 1?
Amer. Math. Monthly, 114(4):344-350, 2007.




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SpezialForschungsBereich SFB F013 | Special Research Program of the FWF - Austrian Science Fund