DLMF:8.10.E7 (Q2563)

From testwiki
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:8.10.E7
No description defined

    Statements

    test
    I = ∫ 0 x t a - 1 ⁢ e t ⁢ d t = Γ ⁡ ( a ) ⁢ x a ⁢ γ * ⁡ ( a , - x ) , 𝐼 superscript subscript 0 𝑥 superscript 𝑡 𝑎 1 superscript 𝑒 𝑡 𝑡 Euler-Gamma 𝑎 superscript 𝑥 𝑎 incomplete-gamma-star 𝑎 𝑥 {\displaystyle{\displaystyle I=\int_{0}^{x}t^{a-1}e^{t}\mathrm{d}t=\Gamma\left% (a\right)x^{a}\gamma^{*}\left(a,-x\right),}}
    0 references
    DLMF id
    DLMF:8.10.E7
    0 references
    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    incomplete gamma function
    test
    γ * ⁡ ( a , z ) incomplete-gamma-star 𝑎 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E6.m2adec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    Q11332
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1fdec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1fdec
    0 references
    Q11338
    test
    I 𝐼 {\displaystyle{\displaystyle I}}
    xml-id
    C8.S10.XMD4.m1dec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2563&oldid=12941"