DLMF:13.3.E28 (Q4362)

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DLMF:13.3.E28
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    Statements

    test
    d n d z n ⁡ ( z b - 1 ⁢ e - z ⁢ U ⁡ ( a , b , z ) ) = ( - 1 ) n ⁢ z b - n - 1 ⁢ e - z ⁢ U ⁡ ( a - n , b - n , z ) . derivative 𝑧 𝑛 superscript 𝑧 𝑏 1 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 1 𝑛 superscript 𝑧 𝑏 𝑛 1 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 𝑎 𝑛 𝑏 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(z^% {b-1}e^{-z}U\left(a,b,z\right)\right)=(-1)^{n}z^{b-n-1}e^{-z}U\left(a-n,b-n,z% \right).}}
    0 references
    DLMF id
    DLMF:13.3.E28
    0 references
    Symbols used
    Kummer confluent hypergeometric function
    test
    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.m2amdec
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    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2amdec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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    Q11559
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1kdec
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