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A Pair of Dual Integral Equations Involving Bessel Functions of the First and the Second Kind

Published online by Cambridge University Press:  20 January 2009

R. P. Srivastav
R. P. Srivastav
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur, (U.P.), India
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In this paper we give a method for the solution of the dual integral equations

where Jv and Yv are Bessel functions of the first and second kind, −½≦α≦½, f1(ρ) and f2(ρ) are known functions and ψ(ξ) is to be determined. Such equations arise in the discussion of boundary value problems for half-spaces containing a cylindrical cavity. For example, let us take the problem of finding a potential function φ(ρ, θ, z) which satisfies Laplace's equation for

subject to the usual regularity conditions and the following boundary conditions:

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 2 , December 1964 , pp. 149 - 158
Copyright
Copyright © Edinburgh Mathematical Society 1964

References

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