DLMF:2.10.E35 (Q1022)

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DLMF:2.10.E35
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    Statements

    Defining formula
    g n = ( 2 π ⁢ sin ⁡ α ) 1 / 2 ⁢ Γ ⁡ ( n + 1 2 ) n ! ⁢ cos ⁡ ( n ⁢ α + 1 2 ⁢ α - 1 4 ⁢ π ) , subscript 𝑔 𝑛 superscript 2 𝜋 𝛼 1 2 Euler-Gamma 𝑛 1 2 𝑛 𝑛 𝛼 1 2 𝛼 1 4 𝜋 {\displaystyle{\displaystyle g_{n}=\left(\frac{2}{\pi\sin\alpha}\right)^{1/2}% \frac{\Gamma\left(n+\frac{1}{2}\right)}{n!}\cos\left(n\alpha+\tfrac{1}{2}% \alpha-\tfrac{1}{4}\pi\right),}}
    0 references
    DLMF id
    DLMF:2.10.E35
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
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    Q11132
    Defining formula
    g n subscript 𝑔 𝑛 {\displaystyle{\displaystyle g_{n}}}
    xml-id
    C2.S10.XMD18.m1ddec
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