DLMF:28.4.E27 (Q8221): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2acdec

Revision as of 14:42, 2 January 2020

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DLMF:28.4.E27
No description defined

    Statements

    Defining formula
    B 2 ⁢ m 2 ⁢ n + 2 ⁢ ( q ) B 2 2 ⁢ n + 2 ⁢ ( q ) = ( - 1 ) m ( m ! ) 2 ⁢ ( q 4 ) m ⁢ q ⁢ π ⁢ ( 1 + O ⁡ ( m - 1 ) ) w I ′ ⁢ ( 1 2 ⁢ π ; b 2 ⁢ n + 2 ⁡ ( q ) , q ) . subscript superscript 𝐵 2 𝑛 2 2 𝑚 𝑞 subscript superscript 𝐵 2 𝑛 2 2 𝑞 superscript 1 𝑚 superscript 𝑚 2 superscript 𝑞 4 𝑚 𝑞 𝜋 1 Big-O superscript 𝑚 1 subscript superscript 𝑤 ′ I 1 2 𝜋 Mathieu-eigenvalue-b 2 𝑛 2 𝑞 𝑞 {\displaystyle{\displaystyle\frac{B^{2n+2}_{2m}(q)}{B^{2n+2}_{2}(q)}=\frac{(-1% )^{m}}{(m!)^{2}}\left(\frac{q}{4}\right)^{m}\frac{q\pi\left(1+O\left(m^{-1}% \right)\right)}{w^{\prime}_{\mbox{\tiny I}}(\frac{1}{2}\pi;b_{2n+2}\left(q% \right),q)}.}}
    0 references
    DLMF id
    DLMF:28.4.E27
    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.m2afdec
    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.m4acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
     
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