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The roots of J−(l + ½) (λη)Jl + ½ (λ) − Jl + ½ (λη) J−(l + ½)(λ) = 0

Published online by Cambridge University Press:  24 October 2008

S. Chandrasekhar  and
Donna Elbert
S. Chandrasekhar
Affiliation:
The Yerkes ObservatoryUniversity of Chicago
Donna Elbert
Affiliation:
The Yerkes ObservatoryUniversity of Chicago
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Extract

Spherical Bessel functions which vanish at x = 1 and x = η (where η is an assigned positive constant less than 1) occur in the solution of many problems in applied mathematics. Such functions can be expressed in terms of Bessel's functions of the half odd integral orders in the form

where λ is a root of the equation

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 3 , July 1953 , pp. 446 - 448
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

(1)Carslaw, H. S. and Jaeger, J. C.Conduction of heat in solids (Oxford, 1947), §73.Google Scholar
(2)Chandrasekhar, S.Phil. Mag. (7), 44 (1953), 233.CrossRefGoogle Scholar
(3)Gray, A. and Mathews, G. B.A treatise on Bessel functions, 2nd ed. (London, 1922), p. 82.Google Scholar
(4)Jahnke, E. and Emde, F.Funktionentafeln (Leipzig, 1933), pp. 274–6.Google Scholar
(5)Mathematical Tables Project (National Bureau of Standards, U.S.A.). Tables of spherical Bessel functions, vols. 1 and 2 (New York, 1947).Google Scholar