DLMF:8.5.E3 (Q2512): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: incomplete gamma function / rank
 
Normal rank
Property / Symbols used: incomplete gamma function / qualifier
 
test:

Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}

\incGamma@{\NVar{a}}{\NVar{z}}
Property / Symbols used: incomplete gamma function / qualifier
 
xml-id: C8.S2.E2.m2adec

Revision as of 12:41, 2 January 2020

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DLMF:8.5.E3
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    Statements

    test
    Γ ⁡ ( a , z ) = e - z ⁢ U ⁡ ( 1 - a , 1 - a , z ) = z a ⁢ e - z ⁢ U ⁡ ( 1 , 1 + a , z ) . incomplete-Gamma 𝑎 𝑧 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 1 𝑎 1 𝑎 𝑧 superscript 𝑧 𝑎 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 1 1 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=e^{-z}U\left(1-a,1-a,z% \right)=z^{a}e^{-z}U\left(1,1+a,z\right).}}
    0 references
    DLMF id
    DLMF:8.5.E3
    0 references
    Symbols used
    Kummer confluent hypergeometric function
    test
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    incomplete gamma function
    test
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2adec
    0 references
     
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