DLMF:13.4.E8 (Q4371): Difference between revisions

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Property / constraint
 

| ph z | < 1 2 π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\frac{1}{2}\pi}}

|\phase{z}|<\frac{1}{2}\pi
Property / constraint: | ph z | < 1 2 π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\frac{1}{2}\pi}} / rank
 
Normal rank

Revision as of 17:45, 30 December 2019

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DLMF:13.4.E8
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    Statements

    U ( a , b , z ) = z c - a 0 e - z t t c - 1 𝐅 1 2 ( a , a - b + 1 ; c ; - t ) d t , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑐 𝑎 superscript subscript 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑐 1 hypergeometric-bold-pFq 2 1 𝑎 𝑎 𝑏 1 𝑐 𝑡 𝑡 {\displaystyle{\displaystyle U\left(a,b,z\right)=z^{c-a}\*\int_{0}^{\infty}e^{% -zt}t^{c-1}{{}_{2}{\mathbf{F}}_{1}}\left(a,a-b+1;c;-t\right)\mathrm{d}t,}}
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    DLMF:13.4.E8
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    | ph z | < 1 2 π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\frac{1}{2}\pi}}
    0 references