DLMF:18.17.E20 (Q5761): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1sdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1qdec

Latest revision as of 14:49, 2 January 2020

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English
DLMF:18.17.E20
No description defined

    Statements

    test
    ∫ 0 1 P n ⁡ ( 1 - 2 ⁢ x 2 ) ⁢ cos ⁡ ( x ⁢ y ) ⁢ d x = ( - 1 ) n ⁢ 1 2 ⁢ π ⁢ J n + 1 2 ⁡ ( 1 2 ⁢ y ) ⁢ J - n - 1 2 ⁡ ( 1 2 ⁢ y ) , superscript subscript 0 1 Legendre-spherical-polynomial 𝑛 1 2 superscript 𝑥 2 𝑥 𝑦 𝑥 superscript 1 𝑛 1 2 𝜋 Bessel-J 𝑛 1 2 1 2 𝑦 Bessel-J 𝑛 1 2 1 2 𝑦 {\displaystyle{\displaystyle\int_{0}^{1}P_{n}\left(1-2x^{2}\right)\cos\left(xy% \right)\mathrm{d}x=(-1)^{n}\tfrac{1}{2}\pi J_{n+\frac{1}{2}}\left(\tfrac{1}{2}% y\right)J_{-n-\frac{1}{2}}\left(\tfrac{1}{2}y\right),}}
    0 references
    DLMF id
    DLMF:18.17.E20
    0 references
    Symbols used
    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.m2acdec
    0 references
    Q10920
    test
    P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r10.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1asdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3asdec
    0 references
    Q11743
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1odec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1sdec
    0 references
    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1qdec
    0 references
     
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