DLMF:5.12.E1 (Q2146): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: beta function / rank
 
Normal rank
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.m1adec
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.m3adec
Property / Symbols used
 
Property / Symbols used: Q11275 / rank
 
Normal rank
Property / Symbols used: Q11275 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11275 / qualifier
 
xml-id: C5.S1.XMD8.m1dec
Property / Symbols used
 
Property / Symbols used: Q11283 / rank
 
Normal rank
Property / Symbols used: Q11283 / qualifier
 
test:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q11283 / qualifier
 
xml-id: C5.S1.XMD9.m1dec

Latest revision as of 18:43, 1 January 2020

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DLMF:5.12.E1
No description defined

    Statements

    test
    B ⁡ ( a , b ) = ∫ 0 1 t a - 1 ⁢ ( 1 - t ) b - 1 ⁢ d t = Γ ⁡ ( a ) ⁢ Γ ⁡ ( b ) Γ ⁡ ( a + b ) . Euler-Beta 𝑎 𝑏 superscript subscript 0 1 superscript 𝑡 𝑎 1 superscript 1 𝑡 𝑏 1 𝑡 Euler-Gamma 𝑎 Euler-Gamma 𝑏 Euler-Gamma 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(a,b\right)=\int_{0}^{1}t^{a-1}(1-t% )^{b-1}\mathrm{d}t=\frac{\Gamma\left(a\right)\Gamma\left(b\right)}{\Gamma\left% (a+b\right)}.}}
    0 references
    DLMF id
    DLMF:5.12.E1
    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
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11275
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C5.S1.XMD8.m1dec
    0 references
    Q11283
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C5.S1.XMD9.m1dec
    0 references
     
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