Two theorems of gauss and allied identities proved arithmetically

George E. Andrews

doi:10.2140/pjm.1972.41.563

Two theorems of gauss and allied identities proved arithmetically

George E. Andrews

Mathematics

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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 language	English (US)
Pages (from-to)	563-578
Number of pages	16
Journal	Pacific Journal of Mathematics
Volume	41
Issue number	3
DOIs	https://doi.org/10.2140/pjm.1972.41.563
State	Published - Jun 1972

All Science Journal Classification (ASJC) codes

General Mathematics

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10.2140/pjm.1972.41.563

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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

Abstract

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