DLMF:12.13.E1 (Q4230)

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DLMF:12.13.E1
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    Statements

    Defining formula
    U ⁡ ( a , x + y ) = e 1 2 ⁢ x ⁢ y + 1 4 ⁢ y 2 ⁢ ∑ m = 0 ∞ ( - y ) m m ! ⁢ U ⁡ ( a - m , x ) , parabolic-U 𝑎 𝑥 𝑦 superscript 𝑒 1 2 𝑥 𝑦 1 4 superscript 𝑦 2 superscript subscript 𝑚 0 superscript 𝑦 𝑚 𝑚 parabolic-U 𝑎 𝑚 𝑥 {\displaystyle{\displaystyle U\left(a,x+y\right)=e^{\frac{1}{2}xy+\frac{1}{4}y% ^{2}}\sum_{m=0}^{\infty}\frac{(-y)^{m}}{m!}U\left(a-m,x\right),}}
    0 references
    DLMF id
    DLMF:12.13.E1
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    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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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.m1adec
    0 references
     
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