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Formula:9010

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Digital Library of Mathematical Functions ID 28.14.E4

q ⁢ c 2 ⁢ m + 2 - ( a - ( ν + 2 ⁢ m ) 2 ) ⁢ c 2 ⁢ m + q ⁢ c 2 ⁢ m - 2 = 0 , 𝑞 subscript 𝑐 2 𝑚 2 𝑎 superscript 𝜈 2 𝑚 2 subscript 𝑐 2 𝑚 𝑞 subscript 𝑐 2 𝑚 2 0 {\displaystyle{\displaystyle{qc_{2m+2}-\left(a-(\nu+2m)^{2}\right)c_{2m}+qc_{2% m-2}=0},}}


Constraint(s)

a = λ ν ⁡ ( q ) , c 2 ⁢ m = c 2 ⁢ m ν ⁢ ( q ) formulae-sequence 𝑎 Mathieu-eigenvalue-lambda 𝜈 𝑞 subscript 𝑐 2 𝑚 superscript subscript 𝑐 2 𝑚 𝜈 𝑞 {\displaystyle{\displaystyle a=\lambda_{\nu}\left(q\right),c_{2m}=c_{2m}^{\nu}% (q)}}

Symbols List

  • λ ν + 2 ⁢ n ⁡ ( q ) Mathieu-eigenvalue-lambda 𝜈 2 𝑛 𝑞 {\displaystyle{\displaystyle\lambda_{\NVar{\nu+2n}}\left(\NVar{q}\right)}} :
  • m 𝑚 {\displaystyle{\displaystyle m}} : integer
  • q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}} : parameter
  • ν 𝜈 {\displaystyle{\displaystyle\nu}} : complex parameter
  • a 𝑎 {\displaystyle{\displaystyle a}} : parameter
  • c 2 ⁢ m ⁢ ( q ) subscript 𝑐 2 𝑚 𝑞 {\displaystyle{\displaystyle c_{2m}(q)}} : coefficients
  •  Edit this on Wikidata

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