Two theorems of gauss and allied identities proved arithmetically

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Abstract

The product formulae of Gauss for the theta functions θ4(0, q)and (1/2)(-q)-⅛θ2(0,(-q)½)have been derived in many ways by analytic means. In this paper these formulae are derived by enumerating certain types of partitions. The enumeration technique is shown to be applicable to more general results, and several important theorems in basic hypergeometric series are proved from suitable enumerations of partitions.

Original languageEnglish (US)
Pages (from-to)563-578
Number of pages16
JournalPacific Journal of Mathematics
Volume41
Issue number3
DOIs
StatePublished - Jun 1972

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Enumeration
Gauss
Partition
Basic Hypergeometric Series
Product formula
Theta Functions
Theorem

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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abstract = "The product formulae of Gauss for the theta functions θ4(0, q)and (1/2)(-q)-⅛θ2(0,(-q)½)have been derived in many ways by analytic means. In this paper these formulae are derived by enumerating certain types of partitions. The enumeration technique is shown to be applicable to more general results, and several important theorems in basic hypergeometric series are proved from suitable enumerations of partitions.",
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Two theorems of gauss and allied identities proved arithmetically. / Andrews, George E.

In: Pacific Journal of Mathematics, Vol. 41, No. 3, 06.1972, p. 563-578.

Research output: Contribution to journalArticle

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