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DLMF:13.3.E23 - MaRDI portal

DLMF:13.3.E23 (Q5054)

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DLMF:13.3.E23
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    Statements

    DLMF defining formula
    d n d z n ⁡ U ⁡ ( a , b , z ) = ( - 1 ) n ⁢ ( a ) n ⁢ U ⁡ ( a + n , b + n , z ) , derivative 𝑧 𝑛 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 1 𝑛 Pochhammer 𝑎 𝑛 Kummer-confluent-hypergeometric-U 𝑎 𝑛 𝑏 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}U\left(a% ,b,z\right)=(-1)^{n}{\left(a\right)_{n}}U\left(a+n,b+n,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.m2ahdec
    0 references
    Q10733
    DLMF defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1afdec
    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.m2ahdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1fdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1vdec
    0 references

    Identifiers

     
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