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

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
Defining formula:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1adec

Revision as of 13:50, 2 January 2020

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DLMF:8.9.E2
No description defined

    Statements

    Defining formula
    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}}}}}}},}}
    0 references
    DLMF id
    DLMF:8.9.E2
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    constraint
    | ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    incomplete gamma function
    Defining formula
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2adec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
     
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