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Formula:9276

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Digital Library of Mathematical Functions ID 29.2.E10

d 2 w d ζ 2 + 1 2 ⁢ ( 1 ζ - e 1 + 1 ζ - e 2 + 1 ζ - e 3 ) ⁢ d w d ζ + g - ν ⁢ ( ν + 1 ) ⁢ ζ 4 ⁢ ( ζ - e 1 ) ⁢ ( ζ - e 2 ) ⁢ ( ζ - e 3 ) ⁢ w = 0 , derivative 𝑤 𝜁 2 1 2 1 𝜁 subscript 𝑒 1 1 𝜁 subscript 𝑒 2 1 𝜁 subscript 𝑒 3 derivative 𝑤 𝜁 𝑔 𝜈 𝜈 1 𝜁 4 𝜁 subscript 𝑒 1 𝜁 subscript 𝑒 2 𝜁 subscript 𝑒 3 𝑤 0 {\displaystyle{\displaystyle{\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}\zeta}^{2}}+% \frac{1}{2}\left(\frac{1}{\zeta-e_{1}}+\frac{1}{\zeta-e_{2}}+\frac{1}{\zeta-e_% {3}}\right)\frac{\mathrm{d}w}{\mathrm{d}\zeta}}+\frac{g-\nu(\nu+1)\zeta}{4(% \zeta-e_{1})(\zeta-e_{2})(\zeta-e_{3})}w=0,}}


Constraint(s)

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 $$x$$
  • ν 𝜈 {\displaystyle{\displaystyle\nu}} : real parameter
  • e j subscript 𝑒 𝑗 {\displaystyle{\displaystyle e_{j}}} : constants
  • g 𝑔 {\displaystyle{\displaystyle g}} : 29.2.E7
  • ζ 𝜁 {\displaystyle{\displaystyle\zeta}} : 29.2.E11
  •  Edit this on Wikidata

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