DLMF:13.7.E4 (Q4412)

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DLMF:13.7.E4
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    Statements

    Defining formula
    U ⁡ ( a , b , z ) = z - a ⁢ ∑ s = 0 n - 1 ( a ) s ⁢ ( a - b + 1 ) s s ! ⁢ ( - z ) - s + ε n ⁢ ( z ) , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑎 superscript subscript 𝑠 0 𝑛 1 Pochhammer 𝑎 𝑠 Pochhammer 𝑎 𝑏 1 𝑠 𝑠 superscript 𝑧 𝑠 subscript 𝜀 𝑛 𝑧 {\displaystyle{\displaystyle U\left(a,b,z\right)=z^{-a}\sum_{s=0}^{n-1}\frac{{% \left(a\right)_{s}}{\left(a-b+1\right)_{s}}}{s!}(-z)^{-s}+\varepsilon_{n}(z),}}
    0 references
    DLMF id
    DLMF:13.7.E4
    0 references
    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.m2abdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1acdec
    0 references
     
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