About the Project

Bartky transformation


(0.002 seconds)

4 matching pages

1: 19.22 Quadratic Transformations
Bartky’s Transformation
2: 19.36 Methods of Computation
Complete cases of Legendre’s integrals and symmetric integrals can be computed with quadratic convergence by the AGM method (including Bartky transformations), using the equations in §19.8(i) and §19.22(ii), respectively. … The function cel ( k c , p , a , b ) is computed by successive Bartky transformations (Bulirsch and Stoer (1968), Bulirsch (1969b)). … Bulirsch (1969a, b) extend Bartky’s transformation to el3 ( x , k c , p ) by expressing it in terms of the first incomplete integral, a complete integral of the third kind, and a more complicated integral to which Bartky’s method can be applied. …
3: 19.2 Definitions
§19.2(iii) Bulirsch’s Integrals
Bulirsch’s integrals are linear combinations of Legendre’s integrals that are chosen to facilitate computational application of Bartky’s transformation (Bartky (1938)). …
4: Bibliography B
  • R. Bulirsch (1969a) An extension of the Bartky-transformation to incomplete elliptic integrals of the third kind. Numer. Math. 13 (3), pp. 266–284.