DLMF:28.22.E3 (Q8368): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q12289 / rank
 
Normal rank
Property / Symbols used: Q12289 / qualifier
 
Defining formula:

C n ( q ) subscript 𝐶 𝑛 𝑞 {\displaystyle{\displaystyle C_{n}(q)}}

C_{n}(q)
Property / Symbols used: Q12289 / qualifier
 
xml-id: C28.S5.XMD3.m1dec

Latest revision as of 15:04, 2 January 2020

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DLMF:28.22.E3
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    Statements

    Mc m ( 2 ) ( z , h ) = 2 π 1 g e , m ( h ) ce m ( 0 , h 2 ) ( - f e , m ( h ) Ce m ( z , h 2 ) + 2 π C m ( h 2 ) Fe m ( z , h 2 ) ) , modified-Mathieu-Mc 2 𝑚 𝑧 2 𝜋 1 subscript 𝑔 𝑒 𝑚 Mathieu-ce 𝑚 0 superscript 2 subscript 𝑓 𝑒 𝑚 modified-Mathieu-Ce 𝑚 𝑧 superscript 2 2 𝜋 subscript 𝐶 𝑚 superscript 2 modified-Mathieu-Fe 𝑚 𝑧 superscript 2 {\displaystyle{\displaystyle{\mathrm{Mc}^{(2)}_{m}}\left(z,h\right)=\sqrt{% \frac{2}{\pi}}\dfrac{1}{g_{\mathit{e},m}(h)\mathrm{ce}_{m}\left(0,h^{2}\right)% }\*\left(-f_{\mathit{e},m}(h)\mathrm{Ce}_{m}\left(z,h^{2}\right)+\dfrac{2}{\pi C% _{m}(h^{2})}\mathrm{Fe}_{m}\left(z,h^{2}\right)\right),}}
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    DLMF:28.22.E3
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    ce n ( z , q ) Mathieu-ce 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    C28.S2.SS6.p1.m7aadec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2abdec
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    Ce ν ( z , q ) modified-Mathieu-Ce 𝜈 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{Ce}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}% \right)}}
    C28.S20.E3.m2aadec
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    Fe n ( z , q ) modified-Mathieu-Fe 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{Fe}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    C28.S20.E6.m2adec
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    Mc n ( j ) ( z , h ) modified-Mathieu-Mc 𝑗 𝑛 𝑧 {\displaystyle{\displaystyle{\mathrm{Mc}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z% },\NVar{h}\right)}}
    C28.S20.E15.m2aadec
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    m 𝑚 {\displaystyle{\displaystyle m}}
    C28.S1.XMD1.m1bdec
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    h {\displaystyle{\displaystyle h}}
    C28.S1.XMD11.m1bdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C28.S1.XMD6.m1bdec
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    g e , n ( h ) subscript 𝑔 𝑒 𝑛 {\displaystyle{\displaystyle g_{\mathit{e},n}(h)}}
    C28.S22.XMD1.m1bdec
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    f e , n ( h ) subscript 𝑓 𝑒 𝑛 {\displaystyle{\displaystyle f_{\mathit{e},n}(h)}}
    C28.S22.XMD2.m1dec
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    C n ( q ) subscript 𝐶 𝑛 𝑞 {\displaystyle{\displaystyle C_{n}(q)}}
    C28.S5.XMD3.m1dec
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