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Zbl 0694.65004
Carlson, B.C.
Landen transformations of integrals. (English)
[A] Asymptotic and computational analysis. Conference in honor of Frank W.J. Olver's 65th birthday, Proc. Int. Symp., Winnipeg/Can. 1989, Lect. Notes Pure Appl. Math. 124, 75-94 (1990).

[For the entire collection see Zbl 0689.00009.] \par The author presents Landen's transformation of integrals. It changes an integral I($\xi)$, depending on parameters $\xi =(\xi\sb 1,\xi\sb 2,...,\xi\sb k)$ into I($\eta)$. Examples for $k=2$ and $k=3$ are presented. \par The practical importance of the method lies in repeating the transformation T: $\xi \to \eta =T$ to get $I(\xi)=I(T\sp n\xi)$ for $n=1,2,..$. Another application comes from the fact that the $\eta$ 's may be real when two of the $\xi$ 's are conjugate complex, and the use of complex arithmetic in the computer can thereby be avoided.
[M.Gaspar]

MSC 2000:: *65D20 Computation of special functions
33E05 Elliptic functions and integrals

Keywords: elliptic integrals; Landen's transformation of integrals

Citations: Zbl 0689.00009

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