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mathematical analysis > functional analysis > operator > integral transform > Abel transform

mathematical analysis > functional analysis > transformation > integral transform > Abel transform

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Abel transform

In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions. The Abel transform of a function f(r) is given by

${\\displaystyle F(y)=2\\int _{y}^{\\infty }{\ rac {f(r)r}{\\sqrt {r^{2}-y^{2}}}}\\,dr.}$

Assuming that f(r) drops to zero more quickly than 1/r, the inverse Abel transform is given by

${\\displaystyle f(r)=-{\ rac {1}{\\pi }}\\int _{r}^{\\infty }{\ rac {dF}{dy}}\\,{\ rac {dy}{\\sqrt {y^{2}-r^{2}}}}.}$

integral transform

transformée d'Abel

francés

URI

http://data.loterre.fr/ark:/67375/PSR-TQC1MD4T-P

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