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

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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

    Defining formula
    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 ℎ 2 𝜋 1 subscript 𝑔 𝑒 𝑚 ℎ Mathieu-ce 𝑚 0 superscript ℎ 2 subscript 𝑓 𝑒 𝑚 ℎ modified-Mathieu-Ce 𝑚 𝑧 superscript ℎ 2 2 𝜋 subscript 𝐶 𝑚 superscript ℎ 2 modified-Mathieu-Fe 𝑚 𝑧 superscript ℎ 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),}}
    0 references
    DLMF id
    DLMF:28.22.E3
    0 references
    Symbols used
    Q12283
    Defining formula
    ce n ⁡ ( z , q ) Mathieu-ce 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S2.SS6.p1.m7aadec
    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
    modified Mathieu function
    Defining formula
    Ce ν ⁡ ( z , q ) modified-Mathieu-Ce 𝜈 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{Ce}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S20.E3.m2aadec
    0 references
    modified Mathieu function
    Defining formula
    Fe n ⁡ ( z , q ) modified-Mathieu-Fe 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{Fe}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S20.E6.m2adec
    0 references
    radial Mathieu function
    Defining formula
    Mc n ( j ) ⁡ ( z , h ) modified-Mathieu-Mc 𝑗 𝑛 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{Mc}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z% },\NVar{h}\right)}}
    xml-id
    C28.S20.E15.m2aadec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1bdec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1bdec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1bdec
    0 references
    Q12302
    Defining formula
    g e , n ⁢ ( h ) subscript 𝑔 𝑒 𝑛 ℎ {\displaystyle{\displaystyle g_{\mathit{e},n}(h)}}
    xml-id
    C28.S22.XMD1.m1bdec
    0 references
    Q12303
    Defining formula
    f e , n ⁢ ( h ) subscript 𝑓 𝑒 𝑛 ℎ {\displaystyle{\displaystyle f_{\mathit{e},n}(h)}}
    xml-id
    C28.S22.XMD2.m1dec
    0 references
    Q12289
    Defining formula
    C n ⁢ ( q ) subscript 𝐶 𝑛 𝑞 {\displaystyle{\displaystyle C_{n}(q)}}
    xml-id
    C28.S5.XMD3.m1dec
    0 references
     
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