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A combinatorial proof of Jacobi’s triple product identity

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Abstract

In this paper, we present a simple combinatorial proof of Jacobi’s triple product identity.

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References

  1. Franklin, F.: Sur le développement du produit infini \((1-x)(1-x^2)(1-x^3)\cdots \). C. R. Acad. Paris Ser. A 92, 448–450 (1881)

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  2. Sylvester, J.J., Franklin, F.: A constructive theory of partitions, arranged in three acts, an interact and an exodion. Am. J. Math. 5(1–4), 251–330 (1882)

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  3. Wright, E.M.: An enumerative proof of an identity of Jacobi. J. Lond. Math. Soc. 40, 55–57 (1965)

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Authors and Affiliations

  1. Department of Mathematics and Statistics, The University of Tennessee at Martin, Martin, TN, USA

    Louis W. Kolitsch & Stephanie Kolitsch

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  1. Louis W. Kolitsch
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  2. Stephanie Kolitsch
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Correspondence to Louis W. Kolitsch.

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Kolitsch, L.W., Kolitsch, S. A combinatorial proof of Jacobi’s triple product identity. Ramanujan J 45, 483–489 (2018). https://doi.org/10.1007/s11139-016-9854-5

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  • DOI: https://doi.org/10.1007/s11139-016-9854-5

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