DLMF:11.10.E3 (Q4020): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
test:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1abdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

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

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11491 / rank
 
Normal rank
Property / Symbols used: Q11491 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11491 / qualifier
 
xml-id: C11.S1.XMD2.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1bdec

Latest revision as of 13:54, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:11.10.E3
No description defined

    Statements

    test
    1 π ⁢ ∫ 0 2 ⁢ π cos ⁡ ( ν ⁢ θ - z ⁢ sin ⁡ θ ) ⁢ d θ = ( 1 + cos ⁡ ( 2 ⁢ π ⁢ ν ) ) ⁢ 𝐉 ν ⁡ ( z ) + sin ⁡ ( 2 ⁢ π ⁢ ν ) ⁢ 𝐄 ν ⁡ ( z ) . 1 𝜋 superscript subscript 0 2 𝜋 𝜈 𝜃 𝑧 𝜃 𝜃 1 2 𝜋 𝜈 Anger-J 𝜈 𝑧 2 𝜋 𝜈 Weber-E 𝜈 𝑧 {\displaystyle{\displaystyle\frac{1}{\pi}\int_{0}^{2\pi}\cos\left(\nu\theta-z% \sin\theta\right)\mathrm{d}\theta=(1+\cos\left(2\pi\nu\right))\,\mathbf{J}_{% \nu}\left(z\right)+\sin\left(2\pi\nu\right)\mathbf{E}_{\nu}\left(z\right).}}
    0 references
    DLMF id
    DLMF:11.10.E3
    0 references
    Symbols used
    Anger function
    test
    𝐉 ν ⁡ ( z ) Anger-J 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E1.m2aadec
    0 references
    Weber function
    test
    𝐄 ν ⁡ ( z ) Weber-E 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E2.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    Q11491
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1bdec
    0 references
    Q11492
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1bdec
    0 references
     
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