DLMF:6.16.E1 (Q2310)

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DLMF:6.16.E1
No description defined

    Statements

    Defining formula
    sin ⁡ x + 1 3 ⁢ sin ⁡ ( 3 ⁢ x ) + 1 5 ⁢ sin ⁡ ( 5 ⁢ x ) + … = { 1 4 ⁢ π , 0 < x < π , 0 , x = 0 , - 1 4 ⁢ π , - π < x < 0 . 𝑥 1 3 3 𝑥 1 5 5 𝑥 … cases 1 4 𝜋 0 𝑥 𝜋 0 𝑥 0 1 4 𝜋 𝜋 𝑥 0 {\displaystyle{\displaystyle\sin x+\tfrac{1}{3}\sin\left(3x\right)+\tfrac{1}{5% }\sin\left(5x\right)+\dots=\begin{cases}\frac{1}{4}\pi,&0<x<\pi,\\ 0,&x=0,\\ -\frac{1}{4}\pi,&-\pi<x<0.\end{cases}}}
    0 references
    DLMF id
    DLMF:6.16.E1
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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.m2adec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
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    Q11307
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C6.S1.XMD1.m1dec
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