DLMF:28.15.E1 (Q8325)

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DLMF:28.15.E1
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    Statements

    Defining formula
    λ ν ⁡ ( q ) = ν 2 + 1 2 ⁢ ( ν 2 - 1 ) ⁢ q 2 + 5 ⁢ ν 2 + 7 32 ⁢ ( ν 2 - 1 ) 3 ⁢ ( ν 2 - 4 ) ⁢ q 4 + 9 ⁢ ν 4 + 58 ⁢ ν 2 + 29 64 ⁢ ( ν 2 - 1 ) 5 ⁢ ( ν 2 - 4 ) ⁢ ( ν 2 - 9 ) ⁢ q 6 + ⋯ . Mathieu-eigenvalue-lambda 𝜈 𝑞 superscript 𝜈 2 1 2 superscript 𝜈 2 1 superscript 𝑞 2 5 superscript 𝜈 2 7 32 superscript superscript 𝜈 2 1 3 superscript 𝜈 2 4 superscript 𝑞 4 9 superscript 𝜈 4 58 superscript 𝜈 2 29 64 superscript superscript 𝜈 2 1 5 superscript 𝜈 2 4 superscript 𝜈 2 9 superscript 𝑞 6 ⋯ {\displaystyle{\displaystyle\lambda_{\nu}\left(q\right)=\nu^{2}+\frac{1}{2(\nu% ^{2}-1)}q^{2}+\frac{5\nu^{2}+7}{32(\nu^{2}-1)^{3}(\nu^{2}-4)}q^{4}+\frac{9\nu^% {4}+58\nu^{2}+29}{64(\nu^{2}-1)^{5}(\nu^{2}-4)(\nu^{2}-9)}q^{6}+\cdots.}}
    0 references
    DLMF id
    DLMF:28.15.E1
    0 references
    Symbols used
    Q12298
    Defining formula
    λ ν + 2 ⁢ n ⁡ ( q ) Mathieu-eigenvalue-lambda 𝜈 2 𝑛 𝑞 {\displaystyle{\displaystyle\lambda_{\NVar{\nu+2n}}\left(\NVar{q}\right)}}
    xml-id
    C28.S12.SS1.p2.m5adec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1dec
    0 references
     
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