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DLMF:8.5.E3 - MaRDI portal

DLMF:8.5.E3 (Q3210)

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DLMF:8.5.E3
No description defined

    Statements

    DLMF defining formula
    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
    Symbols used
    Kummer confluent hypergeometric function
    DLMF defining formula
    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
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    incomplete gamma function
    DLMF 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
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1bdec
    0 references
    parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1bdec
    0 references

    Identifiers

     
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