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Hankel transform

In mathematics, the Hankel transform expresses any given function f(r) as the weighted sum of an infinite number of Bessel functions of the first kind Jν(kr). The Bessel functions in the sum are all of the same order ν, but differ in a scaling factor k along the r axis. The necessary coefficient Fν of each Bessel function in the sum, as a function of the…

Definition, Some Hankel transform pairs & Transforming Laplace's equation

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Overview

Definition

Transforming Laplace's equation

Orthogonality

The Plancherel theorem and Parseval's theorem

Relation to the multidimensional Fourier transform

Relation to the Fourier and Abel transforms

Numerical evaluation

Some Hankel transform pairs

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Hankel transform

Nodes48
Edges47
Triples171
Avg. degree1.96
Density0.041667
Components1

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Hankel transform

Top relations

related to References · 122
Hankel transform → ACM Trans, Agnesi, Alfredo, Algorithm, Am, America, Applied Mathematics Letters, Barakat, Bessel, Bessel Functions, Bibcode, Boca Raton, Calculation, Cerjan, Cerullo, Charles, Computation, Conchello, CRC Press, César
related to Relation to the multidimensional Fourier transform · 9
Hankel transform → Consider, Fourier, Hankel, If, Its, Omega, The Hankel, This, To
related to Transforming Laplace's equation · 8
Hankel transform → Bessel, Hankel, In, Laplace's, Laplacian, The Hankel, Therefore, Under
related to Relation to the Fourier and Abel transforms · 7
Hankel transform → Abel, FHA, Fourier, Hankel, In, The Hankel, This
related to Numerical evaluation · 6
Hankel transform → Fourier, Gamma, Hankel, In, Now, The
related to The Plancherel theorem and Parseval's theorem · 6
Hankel transform → Fν, Gν, Hankel, If, Parseval's, Plancherel
related to Definition · 5
Hankel transform → Bessel, Fν, Hankel, The, The Hankel
related to Domain of definition · 4
Hankel transform → Fourier, Hankel, However, Inverting
related to Alternative definition · 3
Hankel transform → An, Hankel, The
is a · 1
Hankel transform → integral transform and was first developed by the mathematician Hermann Hankel

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Important terminology

transform hankel doi 10 fourier bessel displaystyle functions bibcode function infty 1364 order sum transforms textstyle fast integral coordinates int

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hankel transformis aintegral transform and was first developed by the mathematician Hermann Hankel0.90text
Hankel transformrelated to Alternative definitionAn0.60section
Hankel transformrelated to Alternative definitionHankel0.60section
Hankel transformrelated to Alternative definitionThe0.60section
Hankel transformrelated to DefinitionThe Hankel0.60section
Hankel transformrelated to DefinitionBessel0.60section
Hankel transformrelated to DefinitionThe0.60section
Hankel transformrelated to DefinitionHankel0.60section
Hankel transformrelated to DefinitionFν0.60section
Hankel transformrelated to Domain of definitionInverting0.60section
Hankel transformrelated to Domain of definitionHankel0.60section
Hankel transformrelated to Domain of definitionHowever0.60section

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