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An asymptotic expansion for Bessel functions derived with respect to their order

Published online by Cambridge University Press:  24 October 2008

A. C. Sim
A. C. Sim
Affiliation:
Standard Telecommunications Laboratories, Harlow, Essex
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Extract

Formulae for Bessel derivatives with respect to order have generally been obtained by differentiating integral forms of the Bessel functions. In this note an asymptotic expansion will be derived from the differential equation satisfied by the functions, and it will be obtained in a form which terminates when the order is half an odd integer. Previous discussion of these functions has been restricted to the order one half. (See, for example, Ansell and Fisher (1) and Oberhettinger(2).)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 2 , April 1961 , pp. 284 - 287
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Ansell, P. R., and Fisher, R. A., Note on the numerical evaluation of a Bessel function derivative. Proc. Lond. Math. Soc. 24 (1926), liv–lvi.Google Scholar
(2)Oberhettinger, F., On the derivative of Bessel functions with respect to the order. J. Math. Phys. 37 (1958), 75–8.CrossRefGoogle Scholar
(3)Watson, G. N., A treatise on the theory of Bessel functions, 2nd ed. (Cambridge, 1944).Google Scholar