DLMF:8.5.E2 (Q2511)

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DLMF:8.5.E2
No description defined

    Statements

    Defining formula
    Ξ³ * ⁑ ( a , z ) = e - z ⁒ 𝐌 ⁑ ( 1 , 1 + a , z ) = 𝐌 ⁑ ( a , 1 + a , - z ) . incomplete-gamma-star π‘Ž 𝑧 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-bold-M 1 1 π‘Ž 𝑧 Kummer-confluent-hypergeometric-bold-M π‘Ž 1 π‘Ž 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(a,z\right)=e^{-z}{\mathbf{M}}\left% (1,1+a,z\right)={\mathbf{M}}\left(a,1+a,-z\right).}}
    0 references
    DLMF id
    DLMF:8.5.E2
    0 references
    Symbols used
    Olver’s confluent hypergeometric function
    Defining formula
    𝐌 ⁑ ( a , b , z ) Kummer-confluent-hypergeometric-bold-M π‘Ž 𝑏 𝑧 {\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}
    xml-id
    C13.S2.E3.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    incomplete gamma function
    Defining formula
    Ξ³ * ⁑ ( a , z ) incomplete-gamma-star π‘Ž 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E6.m2adec
    0 references
    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1adec
    0 references
    Q11324
    Defining formula
    a π‘Ž {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1adec
    0 references
     
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