DLMF:13.13.E1 (Q4478)

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DLMF:13.13.E1
No description defined

    Statements

    Defining formula
    ∑ n = 0 ∞ ( a ) n ⁢ y n ( b ) n ⁢ n ! ⁢ M ⁡ ( a + n , b + n , x ) , superscript subscript 𝑛 0 Pochhammer 𝑎 𝑛 superscript 𝑦 𝑛 Pochhammer 𝑏 𝑛 𝑛 Kummer-confluent-hypergeometric-M 𝑎 𝑛 𝑏 𝑛 𝑥 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{{\left(a\right)_{n}}y^{n}% }{{\left(b\right)_{n}}n!}M\left(a+n,b+n,x\right),}}
    0 references
    DLMF id
    DLMF:13.13.E1
    0 references
    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    Defining formula
    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
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1dec
    0 references
    Q11566
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1dec
    0 references
    Q11580
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C13.S1.XMD5.m1dec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
     
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