relations to Jacobian elliptic functions
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1: 22.2 Definitions
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22.2.9
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2: 19.10 Relations to Other Functions
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§19.10(i) Theta and Elliptic Functions
…3: 20.9 Relations to Other Functions
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§20.9(ii) Elliptic Functions and Modular Functions
►See §§22.2 and 23.6(i) for the relations of Jacobian and Weierstrass elliptic functions to theta functions. …4: 19.25 Relations to Other Functions
5: 23.6 Relations to Other Functions
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§23.6(ii) Jacobian Elliptic Functions
…6: 22.15 Inverse Functions
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§22.15(ii) Representations as Elliptic Integrals
…7: Bille C. Carlson
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►This invariance usually replaces sets of twelve equations by sets of three equations and applies also to the relation between the first symmetric elliptic integral and the Jacobian functions.
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8: 22.17 Moduli Outside the Interval [0,1]
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►Jacobian elliptic functions with real moduli in the intervals and , or with purely imaginary moduli are related to functions with moduli in the interval by the following formulas.
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