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Formula:8942

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Digital Library of Mathematical Functions ID 28.6.E15

a m ⁡ ( q ) - b m ⁡ ( q ) = 2 ⁢ q m ( 2 m - 1 ⁢ ( m - 1 ) ! ) 2 ⁢ ( 1 + O ⁡ ( q 2 ) ) . Mathieu-eigenvalue-a 𝑚 𝑞 Mathieu-eigenvalue-b 𝑚 𝑞 2 superscript 𝑞 𝑚 superscript superscript 2 𝑚 1 𝑚 1 2 1 Big-O superscript 𝑞 2 {\displaystyle{\displaystyle a_{m}\left(q\right)-b_{m}\left(q\right)=\frac{2q^% {m}}{\left(2^{m-1}(m-1)!\right)^{2}}\left(1+O\left(q^{2}\right)\right).}}


Constraint(s)

Symbols List

  • O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}} : order not exceeding
  • a n ⁡ ( q ) Mathieu-eigenvalue-a 𝑛 𝑞 {\displaystyle{\displaystyle a_{\NVar{n}}\left(\NVar{q}\right)}} :
  • b n ⁡ ( q ) Mathieu-eigenvalue-b 𝑛 𝑞 {\displaystyle{\displaystyle b_{\NVar{n}}\left(\NVar{q}\right)}} :
  • ! {\displaystyle{\displaystyle!}} :
  • m 𝑚 {\displaystyle{\displaystyle m}} : integer
  • q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}} : 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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