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Formula:9408

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Digital Library of Mathematical Functions ID 29.10.E3

d 2 w d z ′ 2 + ( h ′ - ν ⁢ ( ν + 1 ) ⁢ k ′ 2 ⁢ sn 2 ⁡ ( z ′ , k ′ ) ) ⁢ w = 0 . derivative 𝑤 superscript 𝑧 ′ 2 superscript ℎ ′ 𝜈 𝜈 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sn 2 superscript 𝑧 ′ superscript 𝑘 ′ 𝑤 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z^{\prime}}^{2% }}+(h^{\prime}-\nu(\nu+1){k^{\prime}}^{2}{\operatorname{sn}^{2}}\left(z^{% \prime},k^{\prime}\right))w=0.}}


Constraint(s)

Symbols List

  • sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}} : Jacobian elliptic function
  • d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}} : derivative of $$f$$ with respect to $$x$$
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • h ℎ {\displaystyle{\displaystyle h}} : real parameter
  • k 𝑘 {\displaystyle{\displaystyle k}} : real parameter
  • ν 𝜈 {\displaystyle{\displaystyle\nu}} : real parameter
  • w ⁢ ( z ) 𝑤 𝑧 {\displaystyle{\displaystyle w(z)}} : solution
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:30.
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