DLMF:13.4.E7 (Q4370): Difference between revisions

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Property / constraint
 

a > max ( b - 1 , 0 ) 𝑎 𝑏 1 0 {\displaystyle{\displaystyle\Re a>\max\left(\Re b-1,0\right)}}

\realpart@@{a}>\max\left(\realpart@@{b-1},0\right)
Property / constraint: a > max ( b - 1 , 0 ) 𝑎 𝑏 1 0 {\displaystyle{\displaystyle\Re a>\max\left(\Re b-1,0\right)}} / rank
 
Normal rank

Revision as of 16:45, 30 December 2019

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DLMF:13.4.E7
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    Statements

    U ( a , b , z ) = 2 z 1 2 - 1 2 b Γ ( a ) Γ ( a - b + 1 ) 0 e - t t a - 1 2 b - 1 2 K b - 1 ( 2 z t ) d t , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 2 superscript 𝑧 1 2 1 2 𝑏 Euler-Gamma 𝑎 Euler-Gamma 𝑎 𝑏 1 superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 𝑎 1 2 𝑏 1 2 modified-Bessel-second-kind 𝑏 1 2 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{2z^{\frac{1}{2}-\frac{1% }{2}b}}{\Gamma\left(a\right)\Gamma\left(a-b+1\right)}\*\int_{0}^{\infty}e^{-t}% t^{a-\frac{1}{2}b-\frac{1}{2}}K_{b-1}\left(2\sqrt{zt}\right)\mathrm{d}t,}}
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    a > max ( b - 1 , 0 ) 𝑎 𝑏 1 0 {\displaystyle{\displaystyle\Re a>\max\left(\Re b-1,0\right)}}
    0 references