DLMF:2.6.E4 (Q829): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1abdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec

Latest revision as of 16:09, 1 January 2020

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DLMF:2.6.E4
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    Statements

    0 t α - 1 ( x + t ) α + β d t = Γ ( α ) Γ ( β ) Γ ( α + β ) 1 x β , superscript subscript 0 superscript 𝑡 𝛼 1 superscript 𝑥 𝑡 𝛼 𝛽 𝑡 Euler-Gamma 𝛼 Euler-Gamma 𝛽 Euler-Gamma 𝛼 𝛽 1 superscript 𝑥 𝛽 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{t^{\alpha-1}}{(x+t)^{\alpha% +\beta}}\mathrm{d}t=\frac{\Gamma\left(\alpha\right)\Gamma\left(\beta\right)}{% \Gamma\left(\alpha+\beta\right)}\frac{1}{x^{\beta}},}}
    0 references
    0 references
    α > 0 𝛼 0 {\displaystyle{\displaystyle\Re\alpha>0}}
    0 references
    β > 0 𝛽 0 {\displaystyle{\displaystyle\Re\beta>0}}
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2adec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1abdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3abdec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
    0 references