DLMF:13.2.E14 (Q5001)

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DLMF:13.2.E14
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    Statements

    DLMF defining formula
    U ⁡ ( - n , b , z ) = ( - 1 ) n ⁢ ( b ) n + O ⁡ ( z ) , Kummer-confluent-hypergeometric-U 𝑛 𝑏 𝑧 superscript 1 𝑛 Pochhammer 𝑏 𝑛 Big-O 𝑧 {\displaystyle{\displaystyle U\left(-n,b,z\right)=(-1)^{n}{\left(b\right)_{n}}% +O\left(z\right),}}
    0 references
    Symbols used
    order not exceeding
    DLMF defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    Kummer confluent hypergeometric function
    DLMF 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.m2agdec
    0 references
    Q10733
    DLMF defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1agdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1fdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1mdec
    0 references

    Identifiers

     
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