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A function which satisfies the recurrence relation
together with
is called a hemicylindrical function.
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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