DLMF:8.9.E2 (Q2553): Difference between revisions

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Property / constraint
 

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

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

Revision as of 16:10, 30 December 2019

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DLMF:8.9.E2
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    Statements

    z - a e z Γ ( a , z ) = z - 1 1 + ( 1 - a ) z - 1 1 + z - 1 1 + ( 2 - a ) z - 1 1 + 2 z - 1 1 + ( 3 - a ) z - 1 1 + 3 z - 1 1 + , superscript 𝑧 𝑎 superscript 𝑒 𝑧 incomplete-Gamma 𝑎 𝑧 continued-fraction superscript 𝑧 1 1 continued-fraction 1 𝑎 superscript 𝑧 1 1 continued-fraction superscript 𝑧 1 1 continued-fraction 2 𝑎 superscript 𝑧 1 1 continued-fraction 2 superscript 𝑧 1 1 continued-fraction 3 𝑎 superscript 𝑧 1 1 continued-fraction 3 superscript 𝑧 1 1 {\displaystyle{\displaystyle z^{-a}e^{z}\Gamma\left(a,z\right)=\cfrac{z^{-1}}{% 1+\cfrac{(1-a)z^{-1}}{1+\cfrac{z^{-1}}{1+\cfrac{(2-a)z^{-1}}{1+\cfrac{2z^{-1}}% {1+\cfrac{(3-a)z^{-1}}{1+\cfrac{3z^{-1}}{1+\cdots}}}}}}},}}
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    | ph z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
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