DLMF:25.12.E8 (Q7727)

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DLMF:25.12.E8
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    Statements

    Defining formula
    ∑ n = 1 ∞ cos ⁡ ( n ⁢ θ ) n 2 = π 2 6 - π ⁢ θ 2 + θ 2 4 . superscript subscript 𝑛 1 𝑛 𝜃 superscript 𝑛 2 superscript 𝜋 2 6 𝜋 𝜃 2 superscript 𝜃 2 4 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\frac{\cos\left(n\theta\right)}% {n^{2}}=\frac{\pi^{2}}{6}-\frac{\pi\theta}{2}+\frac{\theta^{2}}{4}.}}
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    DLMF id
    DLMF:25.12.E8
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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.m2acdec
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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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    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1bdec
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