Jacobi identity
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1: 20.4 Values at = 0
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Jacobi’s Identity
…2: 27.13 Functions
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27.13.5
►One of Jacobi’s identities implies that
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►Also, Milne (1996, 2002) announce new infinite families of explicit formulas extending Jacobi’s identities.
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3: Bibliography K
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Cyclic identities for Jacobi elliptic and related functions.
J. Math. Phys. 44 (4), pp. 1822–1841.
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Cyclic identities involving Jacobi elliptic functions.
J. Math. Phys. 43 (7), pp. 3798–3806.
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4: Bibliography B
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A cubic counterpart of Jacobi’s identity and the AGM.
Trans. Amer. Math. Soc. 323 (2), pp. 691–701.
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5: 17.8 Special Cases of Functions
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►Apart from Jacobi’s triple product identity (17.8.1) and the quintuple product identity (17.8.3) (see Cooper (2006) for a review), there also exist higher-order tuple product identities.
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6: 20.3 Graphics
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Figure 20.3.18:
, , .
…1 of is chosen arbitrarily since vanishes identically when .
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7: 20.7 Identities
8: 20.11 Generalizations and Analogs
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►This is the discrete analog of the Poisson identity (§1.8(iv)).
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►This is Jacobi’s inversion problem of §20.9(ii).
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►Each provides an extension of Jacobi’s inversion problem.
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9: 22.8 Addition Theorems
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22.8.1
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22.8.15
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22.8.17
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22.8.23
►For these and related identities see Copson (1935, pp. 415–416).
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