DLMF:8.9.E1 (Q2552): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: incomplete gamma function / rank
 
Normal rank
Property / Symbols used: incomplete gamma function / qualifier
 
Defining formula:

γ * ⁡ ( a , z ) incomplete-gamma-star 𝑎 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}

\scincgamma@{\NVar{a}}{\NVar{z}}
Property / Symbols used: incomplete gamma function / qualifier
 
xml-id: C8.S2.E6.m2adec

Revision as of 13:50, 2 January 2020

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DLMF:8.9.E1
No description defined

    Statements

    Defining formula
    Γ ⁡ ( a + 1 ) ⁢ e z ⁢ γ * ⁡ ( a , z ) = 1 1 - z a + 1 + z a + 2 - ( a + 1 ) ⁢ z a + 3 + 2 ⁢ z a + 4 - ( a + 2 ) ⁢ z a + 5 + 3 ⁢ z a + 6 - ⋯ , Euler-Gamma 𝑎 1 superscript 𝑒 𝑧 incomplete-gamma-star 𝑎 𝑧 continued-fraction 1 1 continued-fraction 𝑧 𝑎 1 continued-fraction 𝑧 𝑎 2 continued-fraction 𝑎 1 𝑧 𝑎 3 continued-fraction 2 𝑧 𝑎 4 continued-fraction 𝑎 2 𝑧 𝑎 5 continued-fraction 3 𝑧 𝑎 6 ⋯ {\displaystyle{\displaystyle\Gamma\left(a+1\right)e^{z}\gamma^{*}\left(a,z% \right)=\cfrac{1}{1-\cfrac{z}{a+1+\cfrac{z}{a+2-\cfrac{(a+1)z}{a+3+\cfrac{2z}{% a+4-\cfrac{(a+2)z}{a+5+\cfrac{3z}{a+6-\cdots}}}}}}},}}
    0 references
    DLMF id
    DLMF:8.9.E1
    0 references
    constraint
    a ≠ - 1 , - 2 , … 𝑎 1 2 … {\displaystyle{\displaystyle a\neq-1,-2,\dots}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    incomplete gamma function
    Defining formula
    γ * ⁡ ( a , z ) incomplete-gamma-star 𝑎 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E6.m2adec
    0 references
     
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