DLMF:28.2.E25 (Q8168)

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DLMF:28.2.E25
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    Statements

    Defining formula
    for  q > 0 : a 0 ⁡ < b 1 ⁡ < a 1 ⁡ < b 2 ⁡ < a 2 ⁡ < b 3 ⁡ < ⋯ , for  q < 0 : a 0 ⁡ < a 1 ⁡ < b 1 ⁡ < b 2 ⁡ < a 2 ⁡ < a 3 ⁡ < ⋯ . for  q > 0 : Mathieu-eigenvalue-a 0 𝑞 Mathieu-eigenvalue-b 1 𝑞 Mathieu-eigenvalue-a 1 𝑞 Mathieu-eigenvalue-b 2 𝑞 Mathieu-eigenvalue-a 2 𝑞 Mathieu-eigenvalue-b 3 𝑞 ⋯ for  q < 0 : Mathieu-eigenvalue-a 0 𝑞 Mathieu-eigenvalue-a 1 𝑞 Mathieu-eigenvalue-b 1 𝑞 Mathieu-eigenvalue-b 2 𝑞 Mathieu-eigenvalue-a 2 𝑞 Mathieu-eigenvalue-a 3 𝑞 ⋯ {\displaystyle{\displaystyle\begin{array}[]{rl}\mbox{for $q>0$:}&a_{0}<b_{1}<a% _{1}<b_{2}<a_{2}<b_{3}<\cdots,\\ \mbox{for $q<0$:}&a_{0}<a_{1}<b_{1}<b_{2}<a_{2}<a_{3}<\cdots.\end{array}}}
    0 references
    DLMF id
    DLMF:28.2.E25
    0 references
    Symbols used
    Q12281
    Defining formula
    a n ⁡ ( q ) Mathieu-eigenvalue-a 𝑛 𝑞 {\displaystyle{\displaystyle a_{\NVar{n}}\left(\NVar{q}\right)}}
    xml-id
    C28.S2.SS5.p1.m3addec
    0 references
    Q12282
    Defining formula
    b n ⁡ ( q ) Mathieu-eigenvalue-b 𝑛 𝑞 {\displaystyle{\displaystyle b_{\NVar{n}}\left(\NVar{q}\right)}}
    xml-id
    C28.S2.SS5.p1.m4addec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1sdec
    0 references
     
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