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Formula:10188

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Digital Library of Mathematical Functions ID 33.2.E1

d 2 w d ρ 2 + ( 1 - 2 ⁢ η ρ - ℓ ⁢ ( ℓ + 1 ) ρ 2 ) ⁢ w = 0 , derivative 𝑤 𝜌 2 1 2 𝜂 𝜌 ℓ ℓ 1 superscript 𝜌 2 𝑤 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}\rho}^{2}}+% \left(1-\frac{2\eta}{\rho}-\frac{\ell(\ell+1)}{\rho^{2}}\right)w=0,}}


Constraint(s)

ℓ = 0 , 1 , 2 , … ℓ 0 1 2 … {\displaystyle{\displaystyle\ell=0,1,2,\dots}}

Symbols List

  • d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}} : derivative of $$f$$ with respect to $$x$$
  • ℓ ℓ {\displaystyle{\displaystyle\ell}} : nonnegative integer
  • ρ 𝜌 {\displaystyle{\displaystyle\rho}} : nonnegative real variable
  • η 𝜂 {\displaystyle{\displaystyle\eta}} : real parameter
  •  Edit this on Wikidata

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