DLMF:8.2.E9 (Q2489): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aadec

Revision as of 13:36, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:8.2.E9
No description defined

    Statements

    Defining formula
    Γ ⁡ ( a , z ⁢ e 2 ⁢ π ⁢ m ⁢ i ) = e 2 ⁢ π ⁢ m ⁢ i ⁢ a ⁢ Γ ⁡ ( a , z ) + ( 1 - e 2 ⁢ π ⁢ m ⁢ i ⁢ a ) ⁢ Γ ⁡ ( a ) . incomplete-Gamma 𝑎 𝑧 superscript 𝑒 2 𝜋 𝑚 𝑖 superscript 𝑒 2 𝜋 𝑚 𝑖 𝑎 incomplete-Gamma 𝑎 𝑧 1 superscript 𝑒 2 𝜋 𝑚 𝑖 𝑎 Euler-Gamma 𝑎 {\displaystyle{\displaystyle\Gamma\left(a,ze^{2\pi mi}\right)=e^{2\pi mia}% \Gamma\left(a,z\right)+(1-e^{2\pi mia})\Gamma\left(a\right).}}
    0 references
    DLMF id
    DLMF:8.2.E9
    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.m2addec
    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
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2489&oldid=38222"