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DLMF:13.3.E26 - MaRDI portal

DLMF:13.3.E26 (Q5057)

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DLMF:13.3.E26
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    Statements

    DLMF defining formula
    ( z ⁢ d d z ⁡ z ) n ⁢ ( z b - a - 1 ⁢ e - z ⁢ U ⁡ ( a , b , z ) ) = ( - 1 ) n ⁢ z b - a + n - 1 ⁢ e - z ⁢ U ⁡ ( a - n , b , z ) , superscript 𝑧 derivative 𝑧 𝑧 𝑛 superscript 𝑧 𝑏 𝑎 1 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 1 𝑛 superscript 𝑧 𝑏 𝑎 𝑛 1 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 𝑎 𝑛 𝑏 𝑧 {\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(z^{b-a-1}e^{-z}U\left(a,b,z\right)\right)=(-1)^{n}z^{b-a+n-1}e^{-z}U% \left(a-n,b,z\right),}}
    0 references
    Symbols used
    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.m2akdec
    0 references
    derivative of $$f$$ with respect to $$x$$
    DLMF 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.m2akdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1idec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1ydec
    0 references

    Identifiers

     
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