pith. sign in

|ζ|+ ϱ2 2(x+x 0) # dxp x2(x+σ) 2 +(x+x 0)2 . Again changing the integration variablex→y=2x(x+σ)+ 2 p x2(x+σ) 2 +(x+x 0)2 (note 2x0 =σ+|ζ|) leads this to Φ(r) GΛ0 = Z ∞ 2x0 dy

with Σ(R) Λ0/R0 = 1 8 2F1 3 2 , 1 2 2, 1−ϱ 2 ! = RD(0, ϱ2, 1) 6π = 1 2π  ϱ2E(κ+)−K(κ +) ϱ(ϱ2 −1) (ϱ >1) K(κ−)−E(κ −) 1−ϱ 2 (ϱ <1) = 1 2π(1−ϱ) "2K(κ1) 1+ϱ −E(κ 1) #

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Potentials of axisymmetric razor-thin disks

physics.class-ph · 2026-04-07 · unverdicted · novelty 7.0

Certain families of razor-thin disk surface densities based on beta distributions and relatives produce gravitational potentials equivalent to linear mass distributions, often via single quadratures or closed forms.

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  • Potentials of axisymmetric razor-thin disks physics.class-ph · 2026-04-07 · unverdicted · none · ref 22

    Certain families of razor-thin disk surface densities based on beta distributions and relatives produce gravitational potentials equivalent to linear mass distributions, often via single quadratures or closed forms.