Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T16:58:28.416Z Has data issue: false hasContentIssue false

Enumerative proofs of certain q-identities

Published online by Cambridge University Press:  18 May 2009

George E. Andrews
Affiliation:
The Pennsylvania State University University Park, Pennsylvania
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Many q-identities have been proved combinatorially. For example

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1967

References

1.Andrews, G. E., On basic hypergeometric series, mock theta functions, and partitions (II); to appear.Google Scholar
2.Cheema, M. S., Vector partitions and combinatorial identities, Math. Comp. 18 (1964), 414420.CrossRefGoogle Scholar
3.Hardy, G. H., Ramanujan (Cambridge University Press, Cambridge, 1940).Google Scholar
4.Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (Oxford University Press, London, 4th ed., 1960).Google Scholar
5.Heine, E., Handbuch der Kugelfunctionen, Band I (Berlin, 1878).Google Scholar
6.Ramanujan, S., Collected works (Cambridge University Press, Cambridge, 1927).Google Scholar
7.Slater, L. J., Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (2) 54 (1952), 147167.CrossRefGoogle Scholar
8.Sylvester, J. J., A constructive theory of partitions, etc., Collected math, papers IV (Cambridge, 1912), 3436.Google Scholar
9.Watson, G. N., The mock theta functions (II), Proc. London Math. Soc. (2) 42 (1937), 274304.CrossRefGoogle Scholar
10.Wright, E. M., An enumerative proof of an identity of Jacobi, J. London Math. Soc. 40 (1965), 5557.CrossRefGoogle Scholar