DLMF:5.13.E1 (Q2158): Difference between revisions

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Property / constraint
 

( a + b ) > 0 𝑎 𝑏 0 {\displaystyle{\displaystyle\Re(a+b)>0}}

\realpart@@{(a+b)}>0
Property / constraint: ( a + b ) > 0 𝑎 𝑏 0 {\displaystyle{\displaystyle\Re(a+b)>0}} / rank
 
Normal rank

Revision as of 17:05, 30 December 2019

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DLMF:5.13.E1
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    Statements

    1 2 π i c - i c + i Γ ( s + a ) Γ ( b - s ) z - s d s = Γ ( a + b ) z a ( 1 + z ) a + b , 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 Euler-Gamma 𝑠 𝑎 Euler-Gamma 𝑏 𝑠 superscript 𝑧 𝑠 𝑠 Euler-Gamma 𝑎 𝑏 superscript 𝑧 𝑎 superscript 1 𝑧 𝑎 𝑏 {\displaystyle{\displaystyle{\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}% \Gamma\left(s+a\right)\Gamma\left(b-s\right)z^{-s}\mathrm{d}s=\frac{\Gamma% \left(a+b\right)z^{a}}{(1+z)^{a+b}}},}}
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    DLMF:5.13.E1
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    ( a + b ) > 0 𝑎 𝑏 0 {\displaystyle{\displaystyle\Re(a+b)>0}}
    0 references