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Formula:3906

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Digital Library of Mathematical Functions ID 10.18.E15

x 3 ⁢ w ′′′ + x ⁢ ( 4 ⁢ x 2 + 1 - 4 ⁢ ν 2 ) ⁢ w ′ + ( 4 ⁢ ν 2 - 1 ) ⁢ w = 0 , superscript 𝑥 3 superscript 𝑤 ′′′ 𝑥 4 superscript 𝑥 2 1 4 superscript 𝜈 2 superscript 𝑤 ′ 4 superscript 𝜈 2 1 𝑤 0 {\displaystyle{\displaystyle x^{3}w^{\prime\prime\prime}+x(4x^{2}+1-4\nu^{2})w% ^{\prime}+(4\nu^{2}-1)w=0,}}


Constraint(s)

w = x ⁢ M ν 2 ⁡ ( x ) 𝑤 𝑥 modulus-Bessel-M 𝜈 2 𝑥 {\displaystyle{\displaystyle w=x{M_{\nu}^{2}}\left(x\right)}}

Symbols List

  • M ν ⁡ ( x ) modulus-Bessel-M 𝜈 𝑥 {\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}} : modulus of Bessel functions
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
  • ν 𝜈 {\displaystyle{\displaystyle\nu}} : complex parameter
  •  Edit this on Wikidata

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