DLMF:13.3.E22 (Q4356)

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DLMF:13.3.E22
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    Statements

    Defining formula
    d d z ⁡ U ⁡ ( a , b , z ) = - a ⁢ U ⁡ ( a + 1 , b + 1 , z ) , derivative 𝑧 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 𝑎 Kummer-confluent-hypergeometric-U 𝑎 1 𝑏 1 𝑧 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}U\left(a,b,z\right)=% -aU\left(a+1,b+1,z\right),}}
    0 references
    DLMF id
    DLMF:13.3.E22
    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.m2agdec
    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.m2agdec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1udec
    0 references
     
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