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Asymptotic Expressions for the Bessel Functions and the Fourier-Bessel Expansions
Published online by Cambridge University Press: 20 January 2009
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Asymptotic Expressions for the Bessel Functions.
From the asymptotic expansion for Ku(z) it follows that, if − π < amp z < π,
This theorem is also true if amp z = ± π; to prove this consider the formula
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- Copyright © Edinburgh Mathematical Society 1920
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* This will be clear if N and M tend to infinity together in such a way that the line joining the origin to the point M + i N makes a finite angle with the imaginary axis; for instance, if M = N.
* When n is not an integer the integral along the ε-axis becomes
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20151030084112390-0121:S0013091500035744_eqnU3.gif?pub-status=live)