DLMF:13.4.E3 (Q4366): Difference between revisions

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Property / constraint
 

a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}

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

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DLMF:13.4.E3
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    Statements

    𝐌 ( a , b , - z ) = z 1 2 - 1 2 b Γ ( a ) 0 e - t t a - 1 2 b - 1 2 J b - 1 ( 2 z t ) d t , Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 superscript 𝑧 1 2 1 2 𝑏 Euler-Gamma 𝑎 superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 𝑎 1 2 𝑏 1 2 Bessel-J 𝑏 1 2 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,-z\right)=\frac{z^{\frac{1}{% 2}-\frac{1}{2}b}}{\Gamma\left(a\right)}\int_{0}^{\infty}e^{-t}t^{a-\frac{1}{2}% b-\frac{1}{2}}J_{b-1}\left(2\sqrt{zt}\right)\mathrm{d}t,}}
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    a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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