## Hankel Transform

Equivalent to a 2-D Fourier Transform with a radially symmetric Kernel, and also called the Fourier-Bessel Transform.

 (1)

Let
 (2) (3)

so that
 (4) (5) (6)

 (7) (8) (9)

Then
 (10)

where is a zeroth order Bessel Function of the First Kind. Therefore, the Hankel transform pairs are
 (11)

 (12)

See also Bessel Function of the First Kind, Fourier Transform, Laplace Transform

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 795, 1985.

Bracewell, R. The Fourier Transform and Its Applications. New York: McGraw-Hill, pp. 244-250, 1965.