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Hemicylindrical Function

A hemicylindrical function is a function S_n(z) which satisfies the recurrence relation

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

together with

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

.

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References

Sonine, N. "Recherches sur les fonctions cylindriques et le développement des fonctions continues en séries." Math. Ann. 16, 1-9 and 71-80, 1880.Watson, G. N. "Hemi-Cylindrical Functions." §10.8 in A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, p. 353, 1966.

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Hemicylindrical Function

Cite this as:

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

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