DLMF:8.6.E9 (Q2523): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older editNewer edit →
imported>Admin
imported>Admin
Property / Symbols used
 
Property / Symbols used: incomplete gamma function / rank
 
Normal rank
Property / Symbols used: incomplete gamma function / qualifier
 
test:

Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}

\incGamma@{\NVar{a}}{\NVar{z}}
Property / Symbols used: incomplete gamma function / qualifier
 
xml-id: C8.S2.E2.m2addec

Revision as of 12:44, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:8.6.E9
No description defined

    Statements

    test
    Γ ⁡ ( - a , z ⁢ e ± π ⁢ i ) = e z ⁢ e ∓ π ⁢ i ⁢ a Γ ⁡ ( 1 + a ) ⁢ ∫ 0 ∞ t a ⁢ e - z ⁢ t t - 1 ⁢ d t , incomplete-Gamma 𝑎 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 superscript 𝑒 𝑧 superscript 𝑒 minus-or-plus 𝜋 imaginary-unit 𝑎 Euler-Gamma 1 𝑎 superscript subscript 0 superscript 𝑡 𝑎 superscript 𝑒 𝑧 𝑡 𝑡 1 𝑡 {\displaystyle{\displaystyle\Gamma\left(-a,ze^{\pm\pi i}\right)=\frac{e^{z}e^{% \mp\pi\mathrm{i}a}}{\Gamma\left(1+a\right)}\int_{0}^{\infty}\frac{t^{a}e^{-zt}% }{t-1}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:8.6.E9
    0 references
    constraint
    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
    0 references
    ℜ ⁡ a > - 1 𝑎 1 {\displaystyle{\displaystyle\Re a>-1}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    incomplete gamma function
    test
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2addec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2523&oldid=12647"