DLMF:13.13.E8 (Q4485)

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DLMF:13.13.E8
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    Statements

    Defining formula
    ( x + y x ) 1 - b ⁢ ∑ n = 0 ∞ ( 1 + a - b ) n ⁢ ( - y / x ) n n ! ⁢ U ⁡ ( a , b - n , x ) , superscript 𝑥 𝑦 𝑥 1 𝑏 superscript subscript 𝑛 0 Pochhammer 1 𝑎 𝑏 𝑛 superscript 𝑦 𝑥 𝑛 𝑛 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑛 𝑥 {\displaystyle{\displaystyle\left(\frac{x+y}{x}\right)^{1-b}\*\sum_{n=0}^{% \infty}\frac{{\left(1+a-b\right)_{n}}(-\ifrac{y}{x})^{n}}{n!}U\left(a,b-n,x% \right),}}
    0 references
    DLMF id
    DLMF:13.13.E8
    0 references
    constraint
    | y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}}
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    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.m2aadec
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    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1agdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5agdec
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