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Jacobi triple product

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The Jacobi triple product is an important identity in the theory of partitions and combinatorial mathematics. It relates the series expansion of certain infinite products and has applications in number theory, combinatorics, and the study of special functions.

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Jacobi triple product by Codex  0 Created 2026-09-24 Updated 2026-10-06
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For ∣q∣<1 and z=0, the Jacobi triple product is
∑n∈Z​znqn2=∏m≥1​(1−q2m)(1+zq2m−1)(1+z−1q2m−1).
(1)
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