f ( r , ϕ ) = 1 4 π 2 R e ∮ d Φ d 2 [ d + r c o s ( ϕ − Φ ) ] 2 × ∫ 0 ∞ ω d ω ∫ − ∞ ∞ d Y d ( d 2 + Y 2 ) 1 / 2 P Φ ( Y ) × e x p [ i ω ( d r s i n ( ϕ − Φ ) d + r c o s ( ϕ − Φ ) − Y ) ] {\displaystyle {f(r,\phi )}={\frac {1}{4\pi ^{2}}}Re\oint d\Phi {\frac {d^{2}}{[d+rcos(\phi -\Phi )]^{2}}}\times \int _{0}^{\infty }\omega d\omega \int _{-\infty }^{\infty }dY{\frac {d}{(d^{2}+Y^{2})^{1/2}}}P_{\Phi }(Y)\times exp[i\omega ({\frac {drsin(\phi -\Phi )}{d+rcos(\phi -\Phi )}}-Y)]}
f ( r , ϕ ) = 1 4 π 2 ∮ d Φ d 2 [ d + r c o s ( ϕ − Φ ) ] 2 × P Φ ( Y ) {\displaystyle {f(r,\phi )}={\frac {1}{4\pi ^{2}}}\oint d\Phi {\frac {d^{2}}{[d+rcos(\phi -\Phi )]^{2}}}\times P_{\Phi }(Y)}
Y ( r , ϕ ) = d r s i n ( ϕ − Φ ) d + r c o s ( ϕ − Φ ) {\displaystyle {Y(r,\phi )}={\frac {drsin(\phi -\Phi )}{d+rcos(\phi -\Phi )}}}
P ( Y ) = ∫ − ∞ ∞ d Y ′ d ( d 2 + Y 2 ) 1 / 2 P Φ ( Y ′ ) × g ( Y − Y ′ ) {\displaystyle {P(Y)}=\int _{-\infty }^{\infty }dY'{\frac {d}{(d^{2}+Y^{2})^{1/2}}}P_{\Phi }(Y')\times g(Y-Y')}
g ( Y ) = R e ∫ 0 ω y 0 d ω ω e x p ( i ω Y ) {\displaystyle {g(Y)}=Re\int _{0}^{\omega _{y0}}d\omega \omega exp(i\omega Y)}
F r − 1 F t [ R f ( t ) ] ( r ) | r | ] {\displaystyle {\mathfrak {F}}_{r}^{-1}{\mathfrak {F}}_{t}[{\mathfrak {R}}f(t)](r)|r|]}
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![{\displaystyle {f(r,\phi )}={\frac {1}{4\pi ^{2}}}\oint d\Phi {\frac {d^{2}}{[d+rcos(\phi -\Phi )]^{2}}}\times P_{\Phi }(Y)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/59696d8ee7f17a644a586ed7896f9b73973b0f4e)
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