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Heuman Lambda Function

Lambda_0(phi|m)=(F(phi|1-m))/(K(1-m))+2/piK(m)Z(phi|1-m),

where phi is the Jacobi amplitude, m is the parameter, Z is the Jacobi zeta function, and F(phi|m^') and K(m) are incomplete and complete elliptic integrals of the first kind.

See also

Elliptic Integral of the First Kind, Jacobi Zeta Function

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References

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 595, 1972.Tölke, F. "Jacobische Zeta- und Heumansche Lambda-Funktionen." §132 in Praktische Funktionenlehre, dritter Band: Jacobische elliptische Funktionen, Legendresche elliptische Normalintegrale und spezielle Weierstraßsche Zeta- und Sigma Funktionen. Berlin: Springer-Verlag, pp. 94-99, 1967.

Referenced on Wolfram|Alpha

Heuman Lambda Function

Cite this as:

Weisstein, Eric W. "Heuman Lambda Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HeumanLambdaFunction.html

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