French translation for "hankel transform"

transformation de hankel

Example Sentences:

	1.	The Hankel transform is one member of the FHA cycle of integral operators. La transformée de Hankel est un membre du cycle Abel-Fourier-Hankel d'opérateurs intégraux.
	2.	The Hankel transform of order zero is essentially the 2-dimensional Fourier transform of a circularly symmetric function. La transformation de Hankel d'ordre 0 est essentiellement la transformation de Fourier sur un espace de dimension 2 d'une fonction ayant une symétrie circulaire.
	3.	The Hankel transform of Zernike polynomials are essentially Bessel Functions (Noll 1976): R n m ( r ) = ( − 1 ) n − m 2 ∫ 0 ∞ J n + 1 ( k ) J m ( k r ) d k {\displaystyle R_{n}^{m}(r)=(-1)^{\frac {n-m}{2}}\int _{0}^{\infty }J_{n+1}(k)J_{m}(kr)\operatorname {d} \!k} for even n − m ≥ 0. Les transformées de Hankel des polynômes de Zernike sont des fonctions de Bessel (Noll 1976): R n m ( r ) = ( − 1 ) n − m 2 ∫ 0 ∞ J n + 1 ( k ) J m ( k r ) d k
	4.	The Hankel transform of order ν of a function f(r) is given by: F ν ( k ) = ∫ 0 ∞ f ( r ) J ν ( k r ) r d r {\displaystyle F_{\nu }(k)=\int _{0}^{\infty }f(r)J_{\nu }(kr)\,r\operatorname {d} \!r} where J ν {\displaystyle J_{\nu }} is the Bessel function of the first kind of order ν {\displaystyle \nu } with ν ≥ − 1 2 {\displaystyle \nu \geq -{\frac {1}{2}}} . La transformation de Hankel d'ordre ν d'une fonction f(r) est donnée par : F ν ( k ) = ∫ 0 ∞ f ( r ) J ν ( k r ) r d r
	5.	For example, in two dimensions, if we define A as the Abel transform operator, F as the Fourier transform operator and H as the zeroth-order Hankel transform operator, then the special case of the Projection-slice theorem for circularly symmetric functions states that: F A = H . {\displaystyle FA=H.\,} In other words, applying the Abel transform to a 1-dimensional function and then applying the Fourier transform to that result is the same as applying the Hankel transform to that function. En deux dimensions, si on note A l'opérateur de la transformation d'Abel, F comme l'opérateur de la transformation de Fourier et H l'opérateur de la transformation de Hankel d'ordre 0, alors le théorème de la tranche centrale (en) appliquées aux fonctions ayant une symétrie circulaire donne : F A = H .
	6.	For example, in two dimensions, if we define A as the Abel transform operator, F as the Fourier transform operator and H as the zeroth-order Hankel transform operator, then the special case of the Projection-slice theorem for circularly symmetric functions states that: F A = H . {\displaystyle FA=H.\,} In other words, applying the Abel transform to a 1-dimensional function and then applying the Fourier transform to that result is the same as applying the Hankel transform to that function. En deux dimensions, si on note A l'opérateur de la transformation d'Abel, F comme l'opérateur de la transformation de Fourier et H l'opérateur de la transformation de Hankel d'ordre 0, alors le théorème de la tranche centrale (en) appliquées aux fonctions ayant une symétrie circulaire donne : F A = H .

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