Bartky transformation

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1: 19.22 Quadratic Transformations

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Bartky’s Transformation

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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 $\mathrm{cel}(k_c,p,a,b)$ is computed by successive Bartky transformations (Bulirsch and Stoer (1968), Bulirsch (1969b)). … ►Bulirsch (1969a, b) extend Bartky’s transformation to $\mathrm{el3}(x,k_c,p)$ 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

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§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

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An extension of the Bartky-transformation to incomplete elliptic integrals of the third kind. Numer. Math. 13 (3), pp. 266–284.

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External Links:

ISSN 0029-599X, Document, MathReview (Y. L. Luke), ZentralBlatt

Referenced by:

§19.1, §19.2(iii), §19.36(ii), §19.36(ii).

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