DLMF:12.8.E12 (Q4149)

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DLMF:12.8.E12
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    Statements

    Defining formula
    d m d z m ⁡ ( e - 1 4 ⁢ z 2 ⁢ V ⁡ ( a , z ) ) = ( - 1 ) m ⁢ ( 1 2 - a ) m ⁢ e - 1 4 ⁢ z 2 ⁢ V ⁡ ( a - m , z ) . derivative 𝑧 𝑚 superscript 𝑒 1 4 superscript 𝑧 2 parabolic-V 𝑎 𝑧 superscript 1 𝑚 Pochhammer 1 2 𝑎 𝑚 superscript 𝑒 1 4 superscript 𝑧 2 parabolic-V 𝑎 𝑚 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{m}}{{\mathrm{d}z}^{m}}\left(e^% {-\frac{1}{4}z^{2}}V\left(a,z\right)\right)=(-1)^{m}{\left(\tfrac{1}{2}-a% \right)_{m}}e^{-\frac{1}{4}z^{2}}V\left(a-m,z\right).}}
    0 references
    DLMF id
    DLMF:12.8.E12
    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.m1aadec
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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.m2acdec
    0 references
     
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