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Hemispherical Function

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HemisphereFunction

The hemisphere function is defined as

H(x,y)={sqrt(a-x^2-y^2) for sqrt(x^2+y^2)<=a; 0 for sqrt(x^2+y^2)>a.
(1)

Watson (1966) defines a hemispherical function as a function S which satisfies the recurrence relations

S_(n-1)(z)-S_(n+1)(z)=2S_n^'(z)
(2)

with

S_1(z)=-S_0^'(z).
(3)

See also

Cylinder Function, Cylindrical Function

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References

Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, p. 353, 1966.

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Hemispherical Function

Cite this as:

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

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