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DLMF:12.11.E2 - MaRDI portal

DLMF:12.11.E2 (Q4915)

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DLMF:12.11.E2
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    Statements

    DLMF defining formula
    τ s = ( 2 ⁢ s + 1 2 - a ) ⁢ π + i ⁢ ln ⁡ ( π - 1 2 ⁢ 2 - a - 1 2 ⁢ Γ ⁡ ( 1 2 + a ) ) , subscript 𝜏 𝑠 2 𝑠 1 2 𝑎 𝜋 𝑖 superscript 𝜋 1 2 superscript 2 𝑎 1 2 Euler-Gamma 1 2 𝑎 {\displaystyle{\displaystyle\tau_{s}=\left(2s+\tfrac{1}{2}-a\right)\pi+i\ln% \left(\pi^{-\frac{1}{2}}2^{-a-\frac{1}{2}}\Gamma\left(\tfrac{1}{2}+a\right)% \right),}}
    0 references
    Symbols defined
    12.11.E2
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
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    nonnegative integer
    DLMF defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C12.S1.XMD5.m1adec
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    real or complex parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1adec
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    Identifiers

     
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