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Schläfli Function

The function giving the volume of the spherical quadrectangular tetrahedron:

V=(pi^2)/8f(pi/p,pi/q,pi/r),
(1)

where

1/2pi^2f(pi/2-x,y,pi/2-z) =sum_(m=1)^infty((D-sinxsinz)/(D+sinxsinz))^m(cos(2mx)-cos(2my)+cos(2mz)-1)/(m^2)-x^2-y^2-z^2,
(2)

and

D=sqrt(cos^2xcos^2z-cos^2y).
(3)

See also

Tetrahedron

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Cite this as:

Weisstein, Eric W. "Schläfli Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SchlaefliFunction.html

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