Jacobian elliptic functions
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31—40 of 55 matching pages
31: 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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32: 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. …33: 19.25 Relations to Other Functions
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►Thus the five permutations induce five transformations of Legendre’s integrals (and also of the Jacobian elliptic functions).
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§19.25(v) Jacobian Elliptic Functions
… ►For the use of -functions with in unifying other properties of Jacobian elliptic functions, see Carlson (2004, 2006a, 2006b, 2008). ►Inversions of 12 elliptic integrals of the first kind, producing the 12 Jacobian elliptic functions, are combined and simplified by using the properties of . … …34: 23.6 Relations to Other Functions
35: 29.10 Lamé Functions with Imaginary Periods
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29.10.3
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36: 29.2 Differential Equations
37: 31.2 Differential Equations
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31.2.8
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38: 29.12 Definitions
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►In the fourth column the variable and modulus of the Jacobian elliptic functions have been suppressed, and denotes a polynomial of degree in (different for each type).
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39: 29.7 Asymptotic Expansions
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►Müller (1966a, b) found three formal asymptotic expansions for a fundamental system of solutions of (29.2.1) (and (29.11.1)) as , one in terms of Jacobian elliptic functions and two in terms of Hermite polynomials.
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40: Bibliography C
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Symmetry in c, d, n of Jacobian elliptic functions.
J. Math. Anal. Appl. 299 (1), pp. 242–253.
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Jacobian elliptic functions as inverses of an integral.
J. Comput. Appl. Math. 174 (2), pp. 355–359.
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Some reformulated properties of Jacobian elliptic functions.
J. Math. Anal. Appl. 323 (1), pp. 522–529.
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Table of integrals of squared Jacobian elliptic functions and reductions of related hypergeometric -functions.
Math. Comp. 75 (255), pp. 1309–1318.
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Power series for inverse Jacobian elliptic functions.
Math. Comp. 77 (263), pp. 1615–1621.
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