DLMF:13.4.E10 (Q4373): Difference between revisions

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Property / constraint
 

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

\realpart@@{(b-a)}>0
Property / constraint: ( b - a ) > 0 𝑏 𝑎 0 {\displaystyle{\displaystyle\Re(b-a)>0}} / rank
 
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Revision as of 16:45, 30 December 2019

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DLMF:13.4.E10
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    𝐌 ( a , b , z ) = e - a π i Γ ( 1 - a ) 2 π i Γ ( b - a ) 1 ( 0 + ) e z t t a - 1 ( 1 - t ) b - a - 1 d t , Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 superscript 𝑒 𝑎 𝜋 imaginary-unit Euler-Gamma 1 𝑎 2 𝜋 imaginary-unit Euler-Gamma 𝑏 𝑎 superscript subscript 1 limit-from 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑎 1 superscript 1 𝑡 𝑏 𝑎 1 𝑡 {\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=e^{-a\pi\mathrm{i}}% \frac{\Gamma\left(1-a\right)}{2\pi\mathrm{i}\Gamma\left(b-a\right)}\int_{1}^{(% 0+)}e^{zt}t^{a-1}{(1-t)^{b-a-1}}\mathrm{d}t,}}
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    ( b - a ) > 0 𝑏 𝑎 0 {\displaystyle{\displaystyle\Re(b-a)>0}}
    0 references