DLMF:8.10.E7 (Q2563): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2addec

Revision as of 12:51, 2 January 2020

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DLMF:8.10.E7
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    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
     
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