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),}}
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    DLMF id
    DLMF:12.8.E9
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