TOPICS
Search

Landen's Transformation

If xsinalpha=sin(2beta-alpha), then

(1+x)int_0^alpha(dphi)/(sqrt(1-x^2sin^2phi))=2int_0^beta(dphi)/(sqrt(1-(4x)/((1+x)^2)sin^2phi)).

See also

Elliptic Integral of the First Kind, Gauss's Transformation

Explore with Wolfram|Alpha

References

Abramowitz, M. and Stegun, I. A. (Eds.). "Ascending Landen Transformation" and "Landen's Transformation." §16.14 and 17.5 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 573-574 and 597-598, 1972.

Referenced on Wolfram|Alpha

Landen's Transformation

Cite this as:

Weisstein, Eric W. "Landen's Transformation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LandensTransformation.html

Subject classifications