DLMF:28.22.E2 (Q8367): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12294 / rank
 
Normal rank
Property / Symbols used: Q12294 / qualifier
 
Defining formula:

h ℎ {\displaystyle{\displaystyle h}}

h
Property / Symbols used: Q12294 / qualifier
 
xml-id: C28.S1.XMD11.m1adec

Revision as of 15:03, 2 January 2020

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DLMF:28.22.E2
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    Statements

    Defining formula
    Ms m ( 1 ) ⁡ ( z , h ) = 2 π ⁢ 1 g o , m ⁢ ( h ) ⁢ se m ′ ⁡ ( 0 , h 2 ) ⁢ Se m ⁡ ( z , h 2 ) , modified-Mathieu-Ms 1 𝑚 𝑧 ℎ 2 𝜋 1 subscript 𝑔 𝑜 𝑚 ℎ diffop Mathieu-se 𝑚 1 0 superscript ℎ 2 modified-Mathieu-Se 𝑚 𝑧 superscript ℎ 2 {\displaystyle{\displaystyle{\mathrm{Ms}^{(1)}_{m}}\left(z,h\right)=\sqrt{% \dfrac{2}{\pi}}\frac{1}{g_{\mathit{o},m}(h)\mathrm{se}_{m}'\left(0,h^{2}\right% )}\mathrm{Se}_{m}\left(z,h^{2}\right),}}
    0 references
    DLMF id
    DLMF:28.22.E2
    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.m8adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    radial Mathieu function
    Defining formula
    Ms n ( j ) ⁡ ( z , h ) modified-Mathieu-Ms 𝑗 𝑛 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z% },\NVar{h}\right)}}
    xml-id
    C28.S20.E16.m2adec
    0 references
    modified Mathieu function
    Defining formula
    Se ν ⁡ ( z , q ) modified-Mathieu-Se 𝜈 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{Se}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S20.E4.m2adec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1adec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1adec
    0 references
     
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