DLMF:28.4.E26 (Q8220): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12271 / rank
 
Normal rank
Property / Symbols used: Q12271 / qualifier
 
Defining formula:

q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}

q=h^{2}
Property / Symbols used: Q12271 / qualifier
 
xml-id: C28.S1.XMD10.m1udec
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.m1vdec
Property / Symbols used
 
Property / Symbols used: Q12276 / rank
 
Normal rank
Property / Symbols used: Q12276 / qualifier
 
Defining formula:

w I ⁢ ( z ; a , q ) subscript 𝑤 I 𝑧 𝑎 𝑞 {\displaystyle{\displaystyle w_{\mbox{\tiny I}}(z;a,q)}}

w_{\mbox{\tiny I}}(z;a,q)
Property / Symbols used: Q12276 / qualifier
 
xml-id: C28.S2.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q12288 / rank
 
Normal rank
Property / Symbols used: Q12288 / qualifier
 
Defining formula:

B m ⁢ ( q ) subscript 𝐵 𝑚 𝑞 {\displaystyle{\displaystyle B_{m}(q)}}

B_{m}(q)
Property / Symbols used: Q12288 / qualifier
 
xml-id: C28.S4.XMD2.m1mdec

Latest revision as of 14:42, 2 January 2020

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DLMF:28.4.E26
No description defined

    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
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1xdec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1udec
    0 references
    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1vdec
    0 references
    Q12276
    Defining formula
    w I ⁢ ( z ; a , q ) subscript 𝑤 I 𝑧 𝑎 𝑞 {\displaystyle{\displaystyle w_{\mbox{\tiny I}}(z;a,q)}}
    xml-id
    C28.S2.XMD3.m1dec
    0 references
    Q12288
    Defining formula
    B m ⁢ ( q ) subscript 𝐵 𝑚 𝑞 {\displaystyle{\displaystyle B_{m}(q)}}
    xml-id
    C28.S4.XMD2.m1mdec
    0 references
     
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