DLMF:5.9.E8 (Q2097): Difference between revisions

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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.m3agdec
Property / Symbols used
 
Property / Symbols used: Q11274 / rank
 
Normal rank
Property / Symbols used: Q11274 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11274 / qualifier
 
xml-id: C5.S1.XMD3.m1adec

Latest revision as of 18:36, 1 January 2020

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DLMF:5.9.E8
No description defined

    Statements

    test
    Γ ⁡ ( 1 + 1 n ) ⁢ cos ⁡ ( π 2 ⁢ n ) = ∫ 0 ∞ cos ⁡ ( t n ) ⁢ d t , Euler-Gamma 1 1 𝑛 𝜋 2 𝑛 superscript subscript 0 superscript 𝑡 𝑛 𝑡 {\displaystyle{\displaystyle\Gamma\left(1+\frac{1}{n}\right)\cos\left(\frac{% \pi}{2n}\right)=\int_{0}^{\infty}\cos\left(t^{n}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:5.9.E8
    0 references
    constraint
    n = 2 , 3 , 4 , … 𝑛 2 3 4 … {\displaystyle{\displaystyle n=2,3,4,\dots}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2agdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    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.m1agdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
    0 references
    Q11274
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C5.S1.XMD3.m1adec
    0 references
     
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