DLMF:28.10.E7 (Q8286): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3afdec

Revision as of 14:51, 2 January 2020

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DLMF:28.10.E7
No description defined

    Statements

    Defining formula
    2 π ⁢ ∫ 0 π / 2 sin ⁡ z ⁢ sin ⁡ t ⁢ sin ⁡ ( 2 ⁢ h ⁢ cos ⁡ z ⁢ cos ⁡ t ) ⁢ se 2 ⁢ n + 2 ⁡ ( t , h 2 ) ⁢ d t = - h ⁢ B 2 2 ⁢ n + 2 ⁢ ( h 2 ) 2 ⁢ se 2 ⁢ n + 2 ′ ⁡ ( 1 2 ⁢ π , h 2 ) ⁢ se 2 ⁢ n + 2 ⁡ ( z , h 2 ) , 2 𝜋 superscript subscript 0 𝜋 2 𝑧 𝑡 2 ℎ 𝑧 𝑡 Mathieu-se 2 𝑛 2 𝑡 superscript ℎ 2 𝑡 ℎ superscript subscript 𝐵 2 2 𝑛 2 superscript ℎ 2 2 diffop Mathieu-se 2 𝑛 2 1 1 2 𝜋 superscript ℎ 2 Mathieu-se 2 𝑛 2 𝑧 superscript ℎ 2 {\displaystyle{\displaystyle\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin z\sin t% \sin\left(2h\cos z\cos t\right)\mathrm{se}_{2n+2}\left(t,h^{2}\right)\mathrm{d% }t=-\frac{hB_{2}^{2n+2}(h^{2})}{2\mathrm{se}_{2n+2}'\left(\frac{1}{2}\pi,h^{2}% \right)}\mathrm{se}_{2n+2}\left(z,h^{2}\right),}}
    0 references
    DLMF id
    DLMF:28.10.E7
    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.m8abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2addec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
    0 references
     
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