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Date: 14-10-2019
2406
Date: 28-8-2018
3392
Date: 11-6-2019
1018
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The cylinder function is defined as
(1) |
The Bessel functions are sometimes also called cylinder functions.
To find the Fourier transform of the cylinder function, let
(2) |
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(3) |
and
(4) |
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(5) |
Then
(6) |
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(7) |
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(8) |
Let , so . Then
(9) |
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(10) |
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(11) |
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(12) |
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(13) |
where is a Bessel function of the first kind.
As defined by Watson (1966), a "cylinder function" is any function which satisfies the recurrence relations
(14) |
(15) |
This class of functions can be expressed in terms of Bessel functions.
REFERENCES:
Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1966.
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