DLMF:13.13.E7 (Q4484)

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DLMF:13.13.E7
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    Statements

    Defining formula
    ∑ n = 0 ∞ ( a ) n ⁢ ( - y ) n n ! ⁢ U ⁡ ( a + n , b + n , x ) , superscript subscript 𝑛 0 Pochhammer 𝑎 𝑛 superscript 𝑦 𝑛 𝑛 Kummer-confluent-hypergeometric-U 𝑎 𝑛 𝑏 𝑛 𝑥 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{{\left(a\right)_{n}}(-y)^% {n}}{n!}U\left(a+n,b+n,x\right),}}
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    DLMF id
    DLMF:13.13.E7
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    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.m2adec
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