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# Cylinder Function

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) (3)

and

 (4) (5)

Then

 (6) (7) (8)

Let , so . Then

 (9) (10) (11) (12) (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.

Bessel Function of the First Kind, Cylindrical Function, Hemispherical Function, Parabolic Cylinder Function

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## References

Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1966.

## Referenced on Wolfram|Alpha

Cylinder Function

## Cite this as:

Weisstein, Eric W. "Cylinder Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CylinderFunction.html