DLMF:28.6.E19 (Q8253)

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DLMF:28.6.E19
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    Statements

    Defining formula
    a - ( 2 ⁢ n + 2 ) 2 - q 2 a - ( 2 ⁢ n ) 2 - q 2 a - ( 2 ⁢ n - 2 ) 2 - ⁢ ⋯ ⁢ q 2 a - 2 2 = - q 2 ( 2 ⁢ n + 4 ) 2 - a - q 2 ( 2 ⁢ n + 6 ) 2 - a - ⋯ , 𝑎 superscript 2 𝑛 2 2 continued-fraction superscript 𝑞 2 𝑎 superscript 2 𝑛 2 continued-fraction superscript 𝑞 2 𝑎 limit-from superscript 2 𝑛 2 2 ⋯ continued-fraction superscript 𝑞 2 𝑎 superscript 2 2 continued-fraction superscript 𝑞 2 superscript 2 𝑛 4 2 𝑎 continued-fraction superscript 𝑞 2 superscript 2 𝑛 6 2 𝑎 ⋯ {\displaystyle{\displaystyle a-(2n+2)^{2}-\cfrac{q^{2}}{a-(2n)^{2}-\cfrac{q^{2% }}{a-(2n-2)^{2}-}}\cdots\cfrac{q^{2}}{a-2^{2}}=-\cfrac{q^{2}}{(2n+4)^{2}-a-% \cfrac{q^{2}}{(2n+6)^{2}-a-\cdots}},}}
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    DLMF id
    DLMF:28.6.E19
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    comment
    Warning: Falling back to standard tex;
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    constraint
    a = b 2 ⁢ n + 2 ⁡ ( q ) 𝑎 Mathieu-eigenvalue-b 2 𝑛 2 𝑞 {\displaystyle{\displaystyle a=b_{2n+2}\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.m4aidec
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