Invariance groups of three term transformations for basic hypergeometric series

Journal of Computational and Applied Mathematics

Volumn 197, Issue 1, 2006, Pages 1-14

  Lievens, S ^a   der Jeugt, J Van ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Basic hypergeometric series; Symmetry group; Three term transformation

Indexed keywords

COMPUTATIONAL GEOMETRY; EQUIVALENCE CLASSES; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; THREE TERM CONTROL SYSTEMS;

BASIC HYPERGEOMETRIC SERIES; SYMMETRY GROUP; THREE TERM TRANSFORMATION;

INVARIANCE;

EID: 33746849046     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.10.024     Document Type: Article

References (13)

1. Beyer W.A., Louck J.D., and Stein P.R. Group theoretical basis of some identities for the generalized hypergeometric series. J. Math. Phys. 28 3 (1987) 497-508
2. Budden F.J. The Fascination of Groups (1972), Cambridge University Press, London, New York
3. Cooper S. A q-analogue of Kummer's 20 relations. J. Math. Anal. Appl. 272 1 (2002) 43-54
4. The GAP Group, GAP-Groups, Algorithms, and Programming, Version 4.4, 2005, 〈http://www.gap-system.org〉.
5. Gasper G., and Rahman M. Basic hypergeometric series, Encyclopedia of Mathematics and its Applications vol. 35 (1990), Cambridge University Press, Cambridge
6. Hamermesh M. Group Theory and its Applications to Physical Problems (1962), Addison-Wesley, MA, Reading
7. Krattenthaler C. HYP and HYPQ: Mathematica packages for the manipulation of binomial sums and hypergeometric series, respectively q-binomial sums and basic hypergeometric series. J. Symbolic Comput. 20 5-6 (1995) 737-744
8. 3-series from the Biedenharn-Elliot identity for s u (1, 1). J. Comput. Appl. Math. 169 2 (2004) 419-430
9. Lievens S., Srinivasa Rao K., and Van der Jeugt J. The finite group of the Kummer solutions. Integral Transforms Spec. Funct. 16 2 (2005) 153-158
10. Slater L.J. Generalized Hypergeometric Functions (1966), Cambridge University Press, Cambridge
11. Van der Jeugt J., and Srinivasa Rao K. Invariance groups of transformations of basic hypergeometric series. J. Math. Phys. 40 12 (1999) 6692-6700
12. Whipple F.J.W. A group of generalized hypergeometric series: relations between 120 allied series of the type F [a, b, c ; d, e]. Proc. London Math. Soc. (2) 23 (1925) 104-114
13. 6. Proc. London Math. Soc. (2) 40 (1936) 336-344