DLMF:13.7.E3 (Q4411)

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DLMF:13.7.E3
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    Statements

    Defining formula
    U ⁡ ( a , b , z ) ∼ z - a ⁢ ∑ s = 0 ∞ ( a ) s ⁢ ( a - b + 1 ) s s ! ⁢ ( - z ) - s , asymptotic-expansion Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑎 superscript subscript 𝑠 0 Pochhammer 𝑎 𝑠 Pochhammer 𝑎 𝑏 1 𝑠 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle U\left(a,b,z\right)\sim z^{-a}\sum_{s=0}^{\infty}% \frac{{\left(a\right)_{s}}{\left(a-b+1\right)_{s}}}{s!}(-z)^{-s},}}
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    DLMF id
    DLMF:13.7.E3
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    constraint
    | ph ⁡ z | ≤ 3 2 ⁢ π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta}}
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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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    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
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