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Formula:8946

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Digital Library of Mathematical Functions ID 28.6.E19

a - ( 2 ⁢ n + 2 ) 2 - q 2 a - ( 2 ⁢ n ) 2 - q 2 a - ( 2 ⁢ n - 2 ) 2 - ⁢ ⋯ ⁢ q 2 a - 2 2 = - q 2 ( 2 ⁢ n + 4 ) 2 - a - q 2 ( 2 ⁢ n + 6 ) 2 - a - ⋯ , 𝑎 superscript 2 𝑛 2 2 continued-fraction superscript 𝑞 2 𝑎 superscript 2 𝑛 2 continued-fraction superscript 𝑞 2 𝑎 limit-from superscript 2 𝑛 2 2 ⋯ continued-fraction superscript 𝑞 2 𝑎 superscript 2 2 continued-fraction superscript 𝑞 2 superscript 2 𝑛 4 2 𝑎 continued-fraction superscript 𝑞 2 superscript 2 𝑛 6 2 𝑎 ⋯ {\displaystyle{\displaystyle a-(2n+2)^{2}-\cfrac{q^{2}}{a-(2n)^{2}-\cfrac{q^{2% }}{a-(2n-2)^{2}-}}\cdots\cfrac{q^{2}}{a-2^{2}}=-\cfrac{q^{2}}{(2n+4)^{2}-a-% \cfrac{q^{2}}{(2n+6)^{2}-a-\cdots}},}}


Constraint(s)

a = b 2 ⁢ n + 2 ⁡ ( q ) 𝑎 Mathieu-eigenvalue-b 2 𝑛 2 𝑞 {\displaystyle{\displaystyle a=b_{2n+2}\left(q\right)}}

Symbols List

  • b n ⁡ ( q ) Mathieu-eigenvalue-b 𝑛 𝑞 {\displaystyle{\displaystyle b_{\NVar{n}}\left(\NVar{q}\right)}} :
  • q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}} : parameter
  • n 𝑛 {\displaystyle{\displaystyle n}} : integer
  • a 𝑎 {\displaystyle{\displaystyle a}} : parameter
  •  Edit this on Wikidata

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