Jacobi elliptic
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11: 22.15 Inverse Functions
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►are denoted respectively by
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►Equations (22.15.1) and (22.15.4), for , are equivalent to (22.15.12) and also to
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12: 22.5 Special Values
13: 22.3 Graphics
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►Line graphs of the functions , , , , , , , , , , , and for representative values of real and real illustrating the near trigonometric (), and near hyperbolic () limits.
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, , and as functions of real arguments and .
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14: 22.2 Definitions
15: 22.10 Maclaurin Series
16: 29.18 Mathematical Applications
17: 29.11 Lamé Wave Equation
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29.11.1
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18: 29.8 Integral Equations
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29.8.1
►where are real, and , , are the Jacobian elliptic functions (§22.2).
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29.8.6
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29.8.7
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29.8.9
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19: 22.18 Mathematical Applications
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22.18.5
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►By use of the functions and , parametrizations of algebraic equations, such as
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►With the identification , , the addition law (22.18.8) is transformed into the addition theorem (22.8.1); see Akhiezer (1990, pp. 42, 45, 73–74) and McKean and Moll (1999, §§2.14, 2.16).
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