The symbol
is called a q-Pochhammer symbol (Andrews
1986, p. 10) since it is a q-analog of the
usual Pochhammer symbol. -series obey beautifully sets of properties, and arise naturally
in the theory of partitions, as well as in many problems
of mathematical physics, especially those enumerating possible numbers of configurations
or states on a lattice. The shorthand notation
Andrews, G. E. q-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics,
and Computer Algebra. Providence, RI: Amer. Math. Soc., 1986.Andrews,
G. E. The
Theory of Partitions. Cambridge, England: Cambridge University Press, 1998.Andrews,
G. E.; Askey, R.; and Roy, R. Special
Functions. Cambridge, England: Cambridge University Press, 1999.Berndt,
B. C. "q-Series." Ch. 27 in Ramanujan's
Notebooks, Part IV. New York:Springer-Verlag, pp. 261-286, 1994.Berndt,
B. C.; Huang, S.-S.; Sohn, J.; and Son, S. H. "Some Theorems on the
Rogers-Ramanujan Continued Fraction in Ramanujan's Lost Notebook." To appears
in Trans. Amer. Math. Soc.Bhatnagar, G. "A Multivariable
View of One-Variable q-Series." In Special Functions and Differential
Equations. Proceedings of the Workshop (WSSF97) held in Madras, January 13-24, 1997)
(Ed. K. S. Rao, R. Jagannathan, G. van den Berghe, and J. Van
der Jeugt). New Delhi, India: Allied Pub., pp. 60-72, 1998.Gasper,
G. "Lecture Notes for an Introductory Minicourse on -Series." 25 Sep 1995. http://arxiv.org/abs/math.CA/9509223.Gasper,
G. "Elementary Derivations of Summation and Transformation Formulas for q-Series."
In Fields Inst. Comm.14 (Ed. M. E. H. Ismail et al. ),
pp. 55-70, 1997.Gasper, G. and Rahman, M. Basic
Hypergeometric Series. Cambridge, England: Cambridge University Press, 1990.Gosper,
R. W. "Experiments and Discoveries in q-Trigonometry." In Symbolic
Computation, Number Theory,Special Functions, Physics and Combinatorics. Proceedings
of the Conference Held at the University of Florida, Gainesville, FL, November 11-13,
1999 (Ed. F. G. Garvan and M. E. H. Ismail). Dordrecht,
Netherlands: Kluwer, pp. 79-105, 2001.Hardy, G. H. and Wright,
E. M. An
Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon
Press, 1979.Hirschhorn, M. D. "Another Short Proof of Ramanujan's
Mod 5 Partition Congruences, and More." Amer. Math. Monthly106,
580-583, 1999.Koekoek, R. and Swarttouw, R. F. The Askey-Scheme
of Hypergeometric Orthogonal Polynomials and its -Analogue. Delft, Netherlands: Technische Universiteit
Delft, Faculty of Technical Mathematics and Informatics Report 98-17, 1-168, 1998.Watson,
G. N. "The Final Problem: An Account of the Mock Theta Functions."
J. London Math. Soc.11, 55-80, 1936.Weisstein, E. W.
"Books about q-Series." http://www.ericweisstein.com/encyclopedias/books/q-Series.html.Wolfram,
S. A
New Kind of Science. Champaign, IL: Wolfram Media, p. 1168,
2002.
-series is series
involving coefficients of the form
, where 
is defined as
is called a q-Pochhammer symbol (Andrews
1986, p. 10) since it is a q-analog of the
usual Pochhammer symbol. 
-series obey beautifully sets of properties, and arise naturally
in the theory of partitions, as well as in many problems
of mathematical physics, especially those enumerating possible numbers of configurations
or states on a lattice. The shorthand notation
-Series." 25 Sep 1995. 
-Analogue. Delft, Netherlands: Technische Universiteit
Delft, Faculty of Technical Mathematics and Informatics Report 98-17, 1-168, 1998.Watson,
G. N. "The Final Problem: An Account of the Mock Theta Functions."
J. London Math. Soc. 11, 55-80, 1936.Weisstein, E. W.
"Books about q-Series."