A note on a Jacobian identity
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- by John A. Ewell PDF
- Proc. Amer. Math. Soc. 126 (1998), 421-423 Request permission
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
- John A. Ewell, Arithmetical consequences of a sextuple product identity, Rocky Mountain J. Math. 25 (1995), no. 4, 1287–1293. MR 1371339, DOI 10.1216/rmjm/1181072146
- G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 5th ed., The Clarendon Press, Oxford University Press, New York, 1979. MR 568909
- E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge University Press, New York, 1973.
Additional Information
- John A. Ewell
- Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115
- Received by editor(s): July 25, 1996
- Communicated by: Hal L. Smith
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 421-423
- MSC (1991): Primary 33D10; Secondary 05A19
- DOI: https://doi.org/10.1090/S0002-9939-98-04527-4
- MathSciNet review: 1451797