DLMF:28.4.E26 (Q8220)

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DLMF:28.4.E26
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    Statements

    Defining formula
    B 2 ⁢ m + 1 2 ⁢ n + 1 ⁢ ( q ) B 1 2 ⁢ n + 1 ⁢ ( q ) = ( - 1 ) m ( ( 1 2 ) m + 1 ) 2 ⁢ ( q 4 ) m + 1 ⁢ 2 ⁢ ( 1 + O ⁡ ( m - 1 ) ) w I ⁢ ( 1 2 ⁢ π ; b 2 ⁢ n + 1 ⁡ ( q ) , q ) , subscript superscript 𝐵 2 𝑛 1 2 𝑚 1 𝑞 subscript superscript 𝐵 2 𝑛 1 1 𝑞 superscript 1 𝑚 superscript Pochhammer 1 2 𝑚 1 2 superscript 𝑞 4 𝑚 1 2 1 Big-O superscript 𝑚 1 subscript 𝑤 I 1 2 𝜋 Mathieu-eigenvalue-b 2 𝑛 1 𝑞 𝑞 {\displaystyle{\displaystyle\frac{B^{2n+1}_{2m+1}(q)}{B^{2n+1}_{1}(q)}=\frac{(% -1)^{m}}{\left({\left(\tfrac{1}{2}\right)_{m+1}}\right)^{2}}\left(\frac{q}{4}% \right)^{m+1}\frac{2\left(1+O\left(m^{-1}\right)\right)}{w_{\mbox{\tiny I}}(% \frac{1}{2}\pi;b_{2n+1}\left(q\right),q)},}}
    0 references
    DLMF id
    DLMF:28.4.E26
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aedec
    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.m4abdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
     
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