DLMF:10.22.E16 (Q3390): Difference between revisions

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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.m1aodec

Revision as of 14:51, 2 January 2020

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English
DLMF:10.22.E16
No description defined

    Statements

    test
    ∫ 0 1 2 ⁢ π J 0 ⁡ ( 2 ⁢ z ⁢ sin ⁡ θ ) ⁢ cos ⁡ ( 2 ⁢ n ⁢ θ ) ⁢ d θ = 1 2 ⁢ π ⁢ J n 2 ⁡ ( z ) , superscript subscript 0 1 2 𝜋 Bessel-J 0 2 𝑧 𝜃 2 𝑛 𝜃 𝜃 1 2 𝜋 Bessel-J 𝑛 2 𝑧 {\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}J_{0}\left(2z\sin\theta% \right)\cos\left(2n\theta\right)\mathrm{d}\theta=\tfrac{1}{2}\pi{J_{n}^{2}}% \left(z\right),}}
    0 references
    DLMF id
    DLMF:10.22.E16
    0 references
    constraint
    n = 0 , 1 , 2 , … 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\ldots}}
    0 references
    Symbols used
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1jdec
    0 references
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2ahdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aodec
    0 references
     
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