DLMF:5.12.E4 (Q2149): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11273 / rank
 
Normal rank
Property / Symbols used: Q11273 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11273 / qualifier
 
xml-id: C5.S1.XMD7.m1dec
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.m1cdec
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.m1cdec

Latest revision as of 18:44, 1 January 2020

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English
DLMF:5.12.E4
No description defined

    Statements

    test
    ∫ 0 1 t a - 1 ⁢ ( 1 - t ) b - 1 ( t + z ) a + b ⁢ d t = B ⁡ ( a , b ) ⁢ ( 1 + z ) - a ⁢ z - b , superscript subscript 0 1 superscript 𝑡 𝑎 1 superscript 1 𝑡 𝑏 1 superscript 𝑡 𝑧 𝑎 𝑏 𝑡 Euler-Beta 𝑎 𝑏 superscript 1 𝑧 𝑎 superscript 𝑧 𝑏 {\displaystyle{\displaystyle\int_{0}^{1}\frac{t^{a-1}(1-t)^{b-1}}{(t+z)^{a+b}}% \mathrm{d}t=\mathrm{B}\left(a,b\right)(1+z)^{-a}z^{-b},}}
    0 references
    DLMF id
    DLMF:5.12.E4
    0 references
    constraint
    | ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
    0 references
    Symbols used
    beta function
    test
    B ⁡ ( a , b ) Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}
    xml-id
    C5.S12.E1.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q11273
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1dec
    0 references
    Q11275
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C5.S1.XMD8.m1cdec
    0 references
    Q11283
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C5.S1.XMD9.m1cdec
    0 references
     
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