DLMF:4.21.E35 (Q1737)

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DLMF:4.21.E35
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    Statements

    Defining formula
    sin ⁡ ( n ⁢ z ) = 2 n - 1 ⁢ ∏ k = 0 n - 1 sin ⁡ ( z + k ⁢ π n ) , 𝑛 𝑧 superscript 2 𝑛 1 superscript subscript product 𝑘 0 𝑛 1 𝑧 𝑘 𝜋 𝑛 {\displaystyle{\displaystyle\sin\left(nz\right)=2^{n-1}\prod_{k=0}^{n-1}\sin% \left(z+\frac{k\pi}{n}\right),}}
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    DLMF id
    DLMF:4.21.E35
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    constraint
    n = 1 , 2 , 3 , … 𝑛 1 2 3 … {\displaystyle{\displaystyle n=1,2,3,\dots}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2avdec
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    Q11219
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C4.S1.XMD1.m1dec
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    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1adec
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    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1qdec
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