DLMF:8.2.E10 (Q2490)

From DRMF
Revision as of 13:37, 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:8.2.E10
No description defined

    Statements

    Defining formula
    e - π ⁢ i ⁢ a ⁢ Γ ⁡ ( a , z ⁢ e π ⁢ i ) - e π ⁢ i ⁢ a ⁢ Γ ⁡ ( a , z ⁢ e - π ⁢ i ) = - 2 ⁢ π ⁢ i Γ ⁡ ( 1 - a ) , superscript 𝑒 𝜋 𝑖 𝑎 incomplete-Gamma 𝑎 𝑧 superscript 𝑒 𝜋 𝑖 superscript 𝑒 𝜋 𝑖 𝑎 incomplete-Gamma 𝑎 𝑧 superscript 𝑒 𝜋 𝑖 2 𝜋 𝑖 Euler-Gamma 1 𝑎 {\displaystyle{\displaystyle e^{-\pi ia}\Gamma\left(a,ze^{\pi i}\right)-e^{\pi ia% }\Gamma\left(a,ze^{-\pi i}\right)=-\frac{2\pi i}{\Gamma\left(1-a\right)},}}
    0 references
    DLMF id
    DLMF:8.2.E10
    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.m2aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2490&oldid=38238"