About the Project

Jacobian normal form

AdvancedHelp

(0.001 seconds)

5 matching pages

1: 22.18 Mathematical Applications
The special case y 2 = ( 1 x 2 ) ( 1 k 2 x 2 ) is in Jacobian normal form. For any two points ( x 1 , y 1 ) and ( x 2 , y 2 ) on this curve, their sum ( x 3 , y 3 ) , always a third point on the curve, is defined by the Jacobi–Abel addition law …
2: 22.15 Inverse Functions
The integrals (22.15.12)–(22.15.14) can be regarded as normal forms for representing the inverse functions. …
3: Bibliography C
  • B. C. Carlson (1964) Normal elliptic integrals of the first and second kinds. Duke Math. J. 31 (3), pp. 405–419.
  • B. C. Carlson (2004) Symmetry in c, d, n of Jacobian elliptic functions. J. Math. Anal. Appl. 299 (1), pp. 242–253.
  • B. C. Carlson (2005) Jacobian elliptic functions as inverses of an integral. J. Comput. Appl. Math. 174 (2), pp. 355–359.
  • B. C. Carlson (2008) Power series for inverse Jacobian elliptic functions. Math. Comp. 77 (263), pp. 1615–1621.
  • S. W. Cunningham (1969) Algorithm AS 24: From normal integral to deviate. Appl. Statist. 18 (3), pp. 290–293.
  • 4: 29.15 Fourier Series and Chebyshev Series
    be the eigenvector corresponding to H m and normalized so that … Since (29.2.5) implies that cos ϕ = sn ( z , k ) , (29.15.1) can be rewritten in the form …The set of coefficients of this polynomial (without normalization) can also be found directly as an eigenvector of an ( n + 1 ) × ( n + 1 ) tridiagonal matrix; see Arscott and Khabaza (1962). …
    5: 31.2 Differential Equations
    §31.2(ii) Normal Form of Heun’s Equation
    §31.2(iii) Trigonometric Form
    §31.2(iv) Doubly-Periodic Forms
    Jacobi’s Elliptic Form
    Weierstrass’s Form