DLMF:13.8.E1 (Q4426)

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DLMF:13.8.E1
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    Statements

    Defining formula
    M ⁡ ( a , b , z ) = ∑ s = 0 n - 1 ( a ) s ( b ) s ⁢ s ! ⁢ z s + O ⁡ ( | b | - n ) . Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 superscript subscript 𝑠 0 𝑛 1 Pochhammer 𝑎 𝑠 Pochhammer 𝑏 𝑠 𝑠 superscript 𝑧 𝑠 Big-O superscript 𝑏 𝑛 {\displaystyle{\displaystyle M\left(a,b,z\right)=\sum_{s=0}^{n-1}\frac{{\left(% a\right)_{s}}}{{\left(b\right)_{s}}s!}z^{s}+O\left(|b|^{-n}\right).}}
    0 references
    DLMF id
    DLMF:13.8.E1
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    Defining formula
    M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2adec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1dec
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    Q11558
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C13.S1.XMD3.m1dec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1dec
    0 references
     
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