Hankel Transform
Equivalent to a 2-D Fourier Transform with a radially symmetric Kernel, and alsocalled the Fourier-Bessel Transform.
 | (1) |
 |  |  | (2) |
 | |  | (3) |
so that
 | |  | (4) |
 | |  | (5) |
 | |  | (6) |
 | |  | (7) |
 | |  | (8) |
 | |  | (9) |
Then
 | |  | |
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|  | ||
|  | ||
|  | ||
|  | (10) |
where
is a zeroth order Bessel Function of the First Kind.Therefore, the Hankel transform pairs are | (11) |
 | (12) |
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.
- Gersgorin Circle Theorem
- G-Function
- g-Function
- Ghost
- Gibbs Constant
- Gibbs Effect
- Gibbs Phenomenon
- Gigantic Prime
- Gilbrat's Distribution
- Gilbreath's Conjecture
- Gill's Method
- Gingerbreadman Map
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- Girko's Circular Law
- Girth
- Giuga Number
- Giuga's Conjecture
- Giuga Sequence
- Glaisher-Kinkelin Constant
- Glide
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- Global C(G;T) Theorem
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- Global Maximum
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