DLMF:13.3.E17 (Q4351)

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DLMF:13.3.E17
No description defined

    Statements

    Defining formula
    ( z ⁢ d d z ⁡ z ) n ⁢ ( z a - 1 ⁢ M ⁡ ( a , b , z ) ) = ( a ) n ⁢ z a + n - 1 ⁢ M ⁡ ( a + n , b , z ) , superscript 𝑧 derivative 𝑧 𝑧 𝑛 superscript 𝑧 𝑎 1 Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 Pochhammer 𝑎 𝑛 superscript 𝑧 𝑎 𝑛 1 Kummer-confluent-hypergeometric-M 𝑎 𝑛 𝑏 𝑧 {\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(z^{a-1}M\left(a,b,z\right)\right)={\left(a\right)_{n}}z^{a+n-1}M\left(a+% n,b,z\right),}}
    0 references
    DLMF id
    DLMF:13.3.E17
    0 references
    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ 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.m2aidec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2abdec
    0 references
    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1adec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1pdec
    0 references
     
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