DLMF:13.2.E3 (Q4293)

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DLMF:13.2.E3
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    Statements

    Defining formula
    𝐌 ⁑ ( a , b , z ) = βˆ‘ s = 0 ∞ ( a ) s Ξ“ ⁑ ( b + s ) ⁒ s ! ⁒ z s , Kummer-confluent-hypergeometric-bold-M π‘Ž 𝑏 𝑧 superscript subscript 𝑠 0 Pochhammer π‘Ž 𝑠 Euler-Gamma 𝑏 𝑠 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=\sum_{s=0}^{\infty}% \frac{{\left(a\right)_{s}}}{\Gamma\left(b+s\right)s!}z^{s},}}
    0 references
    DLMF id
    DLMF:13.2.E3
    0 references
    Symbols used
    gamma function
    Defining formula
    Ξ“ ⁑ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer π‘Ž 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
     
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