Jacobian elliptic-function form
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21: 22 Jacobian Elliptic Functions
Chapter 22 Jacobian Elliptic Functions
…22: 22.3 Graphics
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§22.3(i) Real Variables: Line Graphs
… ►§22.3(iii) Complex ; Real
… ►§22.3(iv) Complex
… ► ► …23: 23.21 Physical Applications
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►In §22.19(ii) it is noted that Jacobian elliptic functions provide a natural basis of solutions for problems in Newtonian classical dynamics with quartic potentials in canonical form
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The Weierstrass function
plays a similar role for cubic potentials in canonical form
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►Another form is obtained by identifying , , as lattice roots (§23.3(i)), and setting
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24: 22.19 Physical Applications
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§22.19(ii) Classical Dynamics: The Quartic Oscillator
… ►§22.19(iii) Nonlinear ODEs and PDEs
… ►§22.19(iv) Tops
… ►§22.19(v) Other Applications
… ►25: 22.12 Expansions in Other Trigonometric Series and Doubly-Infinite Partial Fractions: Eisenstein Series
§22.12 Expansions in Other Trigonometric Series and Doubly-Infinite Partial Fractions: Eisenstein Series
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22.12.2
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22.12.8
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22.12.11
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22.12.13
26: Sidebar 22.SB1: Decay of a Soliton in a Bose–Einstein Condensate
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►Jacobian elliptic functions arise as solutions to certain nonlinear Schrödinger equations, which model many types of wave propagation phenomena.
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27: 22.11 Fourier and Hyperbolic Series
§22.11 Fourier and Hyperbolic Series
… ►In (22.11.7)–(22.11.12) the left-hand sides are replaced by their limiting values at the poles of the Jacobian functions. … ►
22.11.13
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►A related hyperbolic series is
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28: 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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