DLMF:12.11.E2 (Q4218)

From DRMF
Revision as of 15:23, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:12.11.E2
No description defined

    Statements

    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
    DLMF id
    DLMF:12.11.E2
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q11526
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C12.S1.XMD5.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4218&oldid=57281"