DLMF:28.10.E3 (Q8282): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aadec

Revision as of 14:49, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:28.10.E3
No description defined

    Statements

    Defining formula
    2 π ⁢ ∫ 0 π / 2 sin ⁡ ( 2 ⁢ h ⁢ cos ⁡ z ⁢ cos ⁡ t ) ⁢ ce 2 ⁢ n + 1 ⁡ ( t , h 2 ) ⁢ d t = - h ⁢ A 1 2 ⁢ n + 1 ⁢ ( h 2 ) ce 2 ⁢ n + 1 ′ ⁡ ( 1 2 ⁢ π , h 2 ) ⁢ ce 2 ⁢ n + 1 ⁡ ( z , h 2 ) , 2 𝜋 superscript subscript 0 𝜋 2 2 ℎ 𝑧 𝑡 Mathieu-ce 2 𝑛 1 𝑡 superscript ℎ 2 𝑡 ℎ superscript subscript 𝐴 1 2 𝑛 1 superscript ℎ 2 diffop Mathieu-ce 2 𝑛 1 1 1 2 𝜋 superscript ℎ 2 Mathieu-ce 2 𝑛 1 𝑧 superscript ℎ 2 {\displaystyle{\displaystyle\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin\left(2h% \cos z\cos t\right)\mathrm{ce}_{2n+1}\left(t,h^{2}\right)\mathrm{d}t=-\frac{hA% _{1}^{2n+1}(h^{2})}{\mathrm{ce}_{2n+1}'\left(\frac{1}{2}\pi,h^{2}\right)}% \mathrm{ce}_{2n+1}\left(z,h^{2}\right),}}
    0 references
    DLMF id
    DLMF:28.10.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.m7abdec
    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
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8282&oldid=51310"