DLMF:12.8.E9 (Q4146)

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DLMF:12.8.E9
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    Statements

    Defining formula
    d m d z m ⁡ ( e 1 4 ⁢ z 2 ⁢ U ⁡ ( a , z ) ) = ( - 1 ) m ⁢ ( 1 2 + a ) m ⁢ e 1 4 ⁢ z 2 ⁢ U ⁡ ( a + m , z ) , derivative 𝑧 𝑚 superscript 𝑒 1 4 superscript 𝑧 2 parabolic-U 𝑎 𝑧 superscript 1 𝑚 Pochhammer 1 2 𝑎 𝑚 superscript 𝑒 1 4 superscript 𝑧 2 parabolic-U 𝑎 𝑚 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{m}}{{\mathrm{d}z}^{m}}\left(e^% {\frac{1}{4}z^{2}}U\left(a,z\right)\right)=(-1)^{m}{\left(\tfrac{1}{2}+a\right% )_{m}}e^{\frac{1}{4}z^{2}}U\left(a+m,z\right),}}
    0 references
    DLMF id
    DLMF:12.8.E9
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
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    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.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q11320
    Defining formula
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1addec
    0 references
    Q11513
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C12.S1.XMD3.m1hdec
    0 references
    Q11516
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1hdec
    0 references
     
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