DLMF:28.22.E4 (Q8369)

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DLMF:28.22.E4
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    Statements

    Defining formula
    Ms m ( 2 ) ⁡ ( z , h ) = 2 π ⁢ 1 g o , m ⁢ ( h ) ⁢ se m ′ ⁡ ( 0 , h 2 ) ⁢ ( - f o , m ⁢ ( h ) ⁢ Se m ⁡ ( z , h 2 ) - 2 π ⁢ S m ⁢ ( h 2 ) ⁢ Ge m ⁡ ( z , h 2 ) ) . modified-Mathieu-Ms 2 𝑚 𝑧 ℎ 2 𝜋 1 subscript 𝑔 𝑜 𝑚 ℎ diffop Mathieu-se 𝑚 1 0 superscript ℎ 2 subscript 𝑓 𝑜 𝑚 ℎ modified-Mathieu-Se 𝑚 𝑧 superscript ℎ 2 2 𝜋 subscript 𝑆 𝑚 superscript ℎ 2 modified-Mathieu-Ge 𝑚 𝑧 superscript ℎ 2 {\displaystyle{\displaystyle{\mathrm{Ms}^{(2)}_{m}}\left(z,h\right)=\sqrt{% \frac{2}{\pi}}\dfrac{1}{g_{\mathit{o},m}(h)\mathrm{se}_{m}'\left(0,h^{2}\right% )}\*\left(-f_{\mathit{o},m}(h)\mathrm{Se}_{m}\left(z,h^{2}\right)-\dfrac{2}{% \pi S_{m}(h^{2})}\mathrm{Ge}_{m}\left(z,h^{2}\right)\right).}}
    0 references
    DLMF id
    DLMF:28.22.E4
    0 references
    Symbols used
    Q12286
    Defining formula
    se n ⁡ ( z , q ) Mathieu-se 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S2.SS6.p1.m8aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    modified Mathieu function
    Defining formula
    Ge n ⁡ ( z , q ) modified-Mathieu-Ge 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{Ge}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S20.E7.m2adec
    0 references
     
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