DLMF:8.5.E1 (Q2510): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1dec

Latest revision as of 12:40, 2 January 2020

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DLMF:8.5.E1
No description defined

    Statements

    test
    γ ⁡ ( a , z ) = a - 1 ⁢ z a ⁢ e - z ⁢ M ⁡ ( 1 , 1 + a , z ) = a - 1 ⁢ z a ⁢ M ⁡ ( a , 1 + a , - z ) , incomplete-gamma 𝑎 𝑧 superscript 𝑎 1 superscript 𝑧 𝑎 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-M 1 1 𝑎 𝑧 superscript 𝑎 1 superscript 𝑧 𝑎 Kummer-confluent-hypergeometric-M 𝑎 1 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(a,z\right)=a^{-1}z^{a}e^{-z}M\left(1,1% +a,z\right)=a^{-1}z^{a}M\left(a,1+a,-z\right),}}
    0 references
    DLMF id
    DLMF:8.5.E1
    0 references
    constraint
    a ≠ 0 , - 1 , - 2 , … 𝑎 0 1 2 … {\displaystyle{\displaystyle a\neq 0,-1,-2,\dots}}
    0 references
    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    test
    M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    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.E1.m2adec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1dec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1dec
    0 references
     
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