DLMF:28.6.E18 (Q8252)

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DLMF:28.6.E18
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    Statements

    Defining formula
    a - ( 2 ⁢ n + 1 ) 2 - q 2 a - ( 2 ⁢ n - 1 ) 2 - ⁢ ⋯ ⁢ q 2 a - 3 2 - q 2 a - 1 2 + q = - q 2 ( 2 ⁢ n + 3 ) 2 - a - q 2 ( 2 ⁢ n + 5 ) 2 - a - ⋯ , 𝑎 superscript 2 𝑛 1 2 continued-fraction superscript 𝑞 2 𝑎 limit-from superscript 2 𝑛 1 2 ⋯ continued-fraction superscript 𝑞 2 𝑎 superscript 3 2 continued-fraction superscript 𝑞 2 𝑎 superscript 1 2 𝑞 continued-fraction superscript 𝑞 2 superscript 2 𝑛 3 2 𝑎 continued-fraction superscript 𝑞 2 superscript 2 𝑛 5 2 𝑎 ⋯ {\displaystyle{\displaystyle a-(2n+1)^{2}-\cfrac{q^{2}}{a-(2n-1)^{2}-}\cdots% \cfrac{q^{2}}{a-3^{2}-\cfrac{q^{2}}{a-1^{2}+q}}=-\cfrac{q^{2}}{(2n+3)^{2}-a-% \cfrac{q^{2}}{(2n+5)^{2}-a-\cdots}},}}
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    DLMF id
    DLMF:28.6.E18
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    comment
    Warning: Falling back to standard tex;
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    constraint
    a = b 2 ⁢ n + 1 ⁡ ( q ) 𝑎 Mathieu-eigenvalue-b 2 𝑛 1 𝑞 {\displaystyle{\displaystyle a=b_{2n+1}\left(q\right)}}
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    Symbols used
    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.m4ahdec
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    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1qdec
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    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1bdec
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