DLMF:8.14.E3 (Q2636): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1abdec
Property / Symbols used
 
Property / Symbols used: Q11332 / rank
 
Normal rank
Property / Symbols used: Q11332 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11332 / qualifier
 
xml-id: C8.S1.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1bdec

Latest revision as of 13:00, 2 January 2020

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DLMF:8.14.E3
No description defined

    Statements

    test
    ∫ 0 ∞ x a - 1 ⁢ γ ⁡ ( b , x ) ⁢ d x = - Γ ⁡ ( a + b ) a , superscript subscript 0 superscript 𝑥 𝑎 1 incomplete-gamma 𝑏 𝑥 𝑥 Euler-Gamma 𝑎 𝑏 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}x^{a-1}\gamma\left(b,x\right)% \mathrm{d}x=-\frac{\Gamma\left(a+b\right)}{a},}}
    0 references
    DLMF id
    DLMF:8.14.E3
    0 references
    constraint
    ℜ ⁡ a < 0 𝑎 0 {\displaystyle{\displaystyle\Re a<0}}
    0 references
    ℜ ⁡ ( a + b ) > 0 𝑎 𝑏 0 {\displaystyle{\displaystyle\Re(a+b)>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.m2abdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    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.E1.m2aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
    Q11332
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1bdec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1bdec
    0 references
     
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