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A note on a Jacobian identity


Author: John A. Ewell
Journal: Proc. Amer. Math. Soc. 126 (1998), 421-423
MSC (1991): Primary 33D10; Secondary 05A19
MathSciNet review: 1451797
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Abstract: An identity involving eight-fold infinite products, first derived by Jacobi in his theory of theta functions, is the subject of this note. Three similar identities, including one that implies Jacobi's identity, are presented.


References [Enhancements On Off] (What's this?)

  • 1. John A. Ewell, Arithmetical consequences of a sextuple product identity, Rocky Mountain J. Math. 25 (1995), no. 4, 1287–1293. MR 1371339, 10.1216/rmjm/1181072146
  • 2. G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Clarenden Press, Oxford, 1960. MR 81i:10002 (5th edition review)
  • 3. E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge University Press, New York, 1973.

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Additional Information

John A. Ewell
Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04527-4
Keywords: Identities of Jacobi, theta functions
Received by editor(s): July 25, 1996
Communicated by: Hal L. Smith
Article copyright: © Copyright 1998 American Mathematical Society