for elliptic functions
(0.004 seconds)
11—20 of 164 matching pages
11: 22.4 Periods, Poles, and Zeros
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►
§22.4(i) Distribution
… ► … ► … ► ►§22.4(ii) Graphical Interpretation via Glaisher’s Notation
…12: 22.1 Special Notation
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►The functions treated in this chapter are the three principal Jacobian elliptic functions
, , ; the nine subsidiary Jacobian elliptic functions
, , , , , , , , ; the amplitude function
; Jacobi’s epsilon and zeta functions
and .
►The notation , , is due to Gudermann (1838), following Jacobi (1827); that for the subsidiary functions is due to Glaisher (1882).
Other notations for are and with ; see Abramowitz and Stegun (1964) and Walker (1996).
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13: 22.14 Integrals
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§22.14(i) Indefinite Integrals of Jacobian Elliptic Functions
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22.14.1
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§22.14(ii) Indefinite Integrals of Powers of Jacobian Elliptic Functions
… ► ►§22.14(iv) Definite Integrals
…14: 22.18 Mathematical Applications
§22.18 Mathematical Applications
►§22.18(i) Lengths and Parametrization of Plane Curves
… ►Lemniscate
… ► … ►15: 22.7 Landen Transformations
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§22.7(i) Descending Landen Transformation
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22.7.3
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§22.7(ii) Ascending Landen Transformation
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22.7.6
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►
§22.7(iii) Generalized Landen Transformations
…16: 22.5 Special Values
§22.5 Special Values
… ► … ►In these cases the elliptic functions degenerate into elementary trigonometric and hyperbolic functions, respectively. … ►17: 22.13 Derivatives and Differential Equations
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►
§22.13(i) Derivatives
► … ►§22.13(ii) First-Order Differential Equations
… ►
22.13.7
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§22.13(iii) Second-Order Differential Equations
…18: 22.3 Graphics
19: 23.1 Special Notation
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►
►The main functions treated in this chapter are the Weierstrass -function
; the Weierstrass zeta function
; the Weierstrass sigma function
; the elliptic modular function
; Klein’s complete invariant ; Dedekind’s eta function
.
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lattice in . | |
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nome. | |
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