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Formula:8941

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Digital Library of Mathematical Functions ID 28.6.E14

a m ⁡ ( q ) b m ⁡ ( q ) } = m 2 + 1 2 ⁢ ( m 2 - 1 ) ⁢ q 2 + 5 ⁢ m 2 + 7 32 ⁢ ( m 2 - 1 ) 3 ⁢ ( m 2 - 4 ) ⁢ q 4 + 9 ⁢ m 4 + 58 ⁢ m 2 + 29 64 ⁢ ( m 2 - 1 ) 5 ⁢ ( m 2 - 4 ) ⁢ ( m 2 - 9 ) ⁢ q 6 + ⋯ . selection Mathieu-eigenvalue-a 𝑚 𝑞 Mathieu-eigenvalue-b 𝑚 𝑞 superscript 𝑚 2 1 2 superscript 𝑚 2 1 superscript 𝑞 2 5 superscript 𝑚 2 7 32 superscript superscript 𝑚 2 1 3 superscript 𝑚 2 4 superscript 𝑞 4 9 superscript 𝑚 4 58 superscript 𝑚 2 29 64 superscript superscript 𝑚 2 1 5 superscript 𝑚 2 4 superscript 𝑚 2 9 superscript 𝑞 6 ⋯ {\displaystyle{\displaystyle\rselection{a_{m}\left(q\right)\\ b_{m}\left(q\right)}=m^{2}+\frac{1}{2(m^{2}-1)}q^{2}+\frac{5m^{2}+7}{32(m^{2}-% 1)^{3}(m^{2}-4)}q^{4}+\frac{9m^{4}+58m^{2}+29}{64(m^{2}-1)^{5}(m^{2}-4)(m^{2}-% 9)}q^{6}+\cdots.}}


Constraint(s)

Symbols List

  • 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)}} :
  • 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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