Vol. 41, No. 3, 1972

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Two theorems of Gauss and allied identities proved arithmetically

George E. Andrews

Vol. 41 (1972), No. 3, 563–578

The product formulae of Gauss for the theta functions 𝜃4(0,q) and (12)(q)18𝜃2(0,(q)12) 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.

Mathematical Subject Classification 2000
Primary: 10A45
Secondary: 05A17
Received: 22 March 1971
Revised: 31 May 1971
Published: 1 June 1972
George E. Andrews
Department of Mathematics
The Pennsylvania State University
109 McAllister Building
University Park PA 16802-7000
United States