DLMF:28.4.E25 (Q8219): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12279 / rank
 
Normal rank
Property / Symbols used: Q12279 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12279 / qualifier
 
xml-id: C28.S1.XMD2.m1udec

Revision as of 14:41, 2 January 2020

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DLMF:28.4.E25
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    Statements

    Defining formula
    A 2 ⁢ m + 1 2 ⁢ n + 1 ⁢ ( q ) A 1 2 ⁢ n + 1 ⁢ ( q ) = ( - 1 ) m + 1 ( ( 1 2 ) m + 1 ) 2 ⁢ ( q 4 ) m + 1 ⁢ 2 ⁢ ( 1 + O ⁡ ( m - 1 ) ) w II ′ ⁢ ( 1 2 ⁢ π ; a 2 ⁢ n + 1 ⁡ ( q ) , q ) , subscript superscript 𝐴 2 𝑛 1 2 𝑚 1 𝑞 subscript superscript 𝐴 2 𝑛 1 1 𝑞 superscript 1 𝑚 1 superscript Pochhammer 1 2 𝑚 1 2 superscript 𝑞 4 𝑚 1 2 1 Big-O superscript 𝑚 1 subscript superscript 𝑤 ′ II 1 2 𝜋 Mathieu-eigenvalue-a 2 𝑛 1 𝑞 𝑞 {\displaystyle{\displaystyle\frac{A^{2n+1}_{2m+1}(q)}{A^{2n+1}_{1}(q)}=\frac{(% -1)^{m+1}}{\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^{\prime}_{\mbox{% \tiny II}}(\frac{1}{2}\pi;a_{2n+1}\left(q\right),q)},}}
    0 references
    DLMF id
    DLMF:28.4.E25
    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.m2addec
    0 references
    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.m3acdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1wdec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1tdec
    0 references
    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1udec
    0 references
     
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