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Formula:9027

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Digital Library of Mathematical Functions ID 28.20.E2

( ζ 2 - 1 ) ⁢ w ′′ + ζ ⁢ w ′ + ( 4 ⁢ q ⁢ ζ 2 - 2 ⁢ q - a ) ⁢ w = 0 , superscript 𝜁 2 1 superscript 𝑤 ′′ 𝜁 superscript 𝑤 ′ 4 𝑞 superscript 𝜁 2 2 𝑞 𝑎 𝑤 0 {\displaystyle{\displaystyle{(\zeta^{2}-1)w^{\prime\prime}+\zeta w^{\prime}+% \left(4q\zeta^{2}-2q-a\right)w=0},}}


Constraint(s)

ζ = cosh ⁡ z 𝜁 𝑧 {\displaystyle{\displaystyle\zeta=\cosh z}}

Symbols List

  • cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}} : hyperbolic cosine function
  • q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}} : parameter
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • a 𝑎 {\displaystyle{\displaystyle a}} : parameter
  • w ⁢ ( z ) 𝑤 𝑧 {\displaystyle{\displaystyle w(z)}} : Mathieu’s equation 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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