DLMF:13.6.E6 (Q4393)

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DLMF:13.6.E6
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    Statements

    Defining formula
    U ⁡ ( a , a , z ) = z 1 - a ⁢ U ⁡ ( 1 , 2 - a , z ) = z 1 - a ⁢ e z ⁢ E a ⁡ ( z ) = e z ⁢ Γ ⁡ ( 1 - a , z ) . Kummer-confluent-hypergeometric-U 𝑎 𝑎 𝑧 superscript 𝑧 1 𝑎 Kummer-confluent-hypergeometric-U 1 2 𝑎 𝑧 superscript 𝑧 1 𝑎 superscript 𝑒 𝑧 exponential-integral-En 𝑎 𝑧 superscript 𝑒 𝑧 incomplete-Gamma 1 𝑎 𝑧 {\displaystyle{\displaystyle U\left(a,a,z\right)=z^{1-a}U\left(1,2-a,z\right)=% z^{1-a}e^{z}E_{a}\left(z\right)=e^{z}\Gamma\left(1-a,z\right).}}
    0 references
    DLMF id
    DLMF:13.6.E6
    0 references
    Symbols used
    Kummer confluent hypergeometric function
    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.m2abdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    generalized exponential integral
    Defining formula
    E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C8.S19.E1.m2adec
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    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
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    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1edec
    0 references
     
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