DLMF:36.7.E3 (Q9936)

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DLMF:36.7.E3
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    Statements

    Defining formula
    3 ⁢ π ⁢ ( 8 ⁢ n + 5 ) 9 + 8 ⁢ ξ n ⁢ ξ n 3 / 2 = 27 16 ⁢ ( 3 2 ) 1 / 2 ⁢ ( ln ⁡ ( 1 ξ n ) + 3 ⁢ ln ⁡ ( 3 2 ) ) . 3 𝜋 8 𝑛 5 9 8 subscript 𝜉 𝑛 superscript subscript 𝜉 𝑛 3 2 27 16 superscript 3 2 1 2 1 subscript 𝜉 𝑛 3 3 2 {\displaystyle{\displaystyle\frac{3\pi(8n+5)}{9+8\xi_{n}}\xi_{n}^{3/2}=\dfrac{% 27}{16}\left(\dfrac{3}{2}\right)^{1/2}\left(\ln\left(\frac{1}{\xi_{n}}\right)+% 3\ln\left(\dfrac{3}{2}\right)\right).}}
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    DLMF id
    DLMF:36.7.E3
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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.m2abdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
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    Q12755
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C36.S1.XMD3.m1bdec
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