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A Bessel function inequality*

Published online by Cambridge University Press:  14 November 2011

A. D. Rawlins
A. D. Rawlins
Affiliation:
Department of Mathematics, University of Dundee
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Synopsis

This paper proves some inequalities for the imaginary part of the transcendental function in a simply connected sector of the complex z-plane, where 0 < v < 1, and part of the boundary depends on v. These inequalities arose in a work of Everitt and Jones [1] which was on a general integral inequality. We give an alternative method of proving these Bessel function inequalities.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 3-4 , 1978 , pp. 187 - 194
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Everitt, W. N. and Jones, D. S.On an integral inequality. Proc. Roy. Soc. London Sect. A 357 (1977), 271–288.Google Scholar
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3Everitt, W. N.On an extension to an integro-differential inequality of Hardy, Littlewood and Polya. Proc. Roy. Soc. Edinburgh Sect. A 69 (1972), 295–333.Google Scholar
4Watson, G. N.A treatise on the theory of Bessel functions (Cambridge: University Press, 1944).Google Scholar
5Erdélyi, A. et al. Higher transcendental functions 2 (New York: McGraw-Hill, 1953).Google Scholar
6Titchmarch, E. C.The theory of functions, 2nd edn (Oxford: Univ. Press, 1939).Google Scholar