DLMF:28.22.E7 (Q8372): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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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.m2afdec
Property / Symbols used
 
Property / Symbols used: Q12284 / rank
 
Normal rank
Property / Symbols used: Q12284 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12284 / qualifier
 
xml-id: C28.S1.XMD1.m1fdec
Property / Symbols used
 
Property / Symbols used: Q12294 / rank
 
Normal rank
Property / Symbols used: Q12294 / qualifier
 
Defining formula:

h {\displaystyle{\displaystyle h}}

h
Property / Symbols used: Q12294 / qualifier
 
xml-id: C28.S1.XMD11.m1fdec
Property / Symbols used
 
Property / Symbols used: Q12302 / rank
 
Normal rank
Property / Symbols used: Q12302 / qualifier
 
Defining formula:

g e , n ( h ) subscript 𝑔 𝑒 𝑛 {\displaystyle{\displaystyle g_{\mathit{e},n}(h)}}

g_{\mathit{e},n}(h)
Property / Symbols used: Q12302 / qualifier
 
xml-id: C28.S22.XMD1.m1fdec
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.m1dec

Latest revision as of 15:05, 2 January 2020

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DLMF:28.22.E7
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    Statements

    g o , 2 m + 1 ( h ) = ( - 1 ) m 2 π se 2 m + 1 ( 1 2 π , h 2 ) h B 1 2 m + 1 ( h 2 ) , subscript 𝑔 𝑜 2 𝑚 1 superscript 1 𝑚 2 𝜋 Mathieu-se 2 𝑚 1 1 2 𝜋 superscript 2 superscript subscript 𝐵 1 2 𝑚 1 superscript 2 {\displaystyle{\displaystyle g_{\mathit{o},2m+1}(h)=(-1)^{m}\sqrt{\dfrac{2}{% \pi}}\dfrac{\mathrm{se}_{2m+1}\left(\frac{1}{2}\pi,h^{2}\right)}{hB_{1}^{2m+1}% (h^{2})},}}
    0 references
    DLMF:28.22.E7
    0 references
    se n ( z , q ) Mathieu-se 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    C28.S2.SS6.p1.m8abdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2afdec
    0 references
    m 𝑚 {\displaystyle{\displaystyle m}}
    C28.S1.XMD1.m1fdec
    0 references
    h {\displaystyle{\displaystyle h}}
    C28.S1.XMD11.m1fdec
    0 references
    g e , n ( h ) subscript 𝑔 𝑒 𝑛 {\displaystyle{\displaystyle g_{\mathit{e},n}(h)}}
    C28.S22.XMD1.m1fdec
    0 references
    B m ( q ) subscript 𝐵 𝑚 𝑞 {\displaystyle{\displaystyle B_{m}(q)}}
    C28.S4.XMD2.m1dec
    0 references