DLMF:12.13.E4 (Q4233)

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DLMF:12.13.E4
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    Statements

    Defining formula
    V ⁡ ( a , x + y ) = e - 1 2 ⁢ x ⁢ y - 1 4 ⁢ y 2 ⁢ ∑ m = 0 ∞ y m m ! ⁢ V ⁡ ( a + m , x ) . parabolic-V 𝑎 𝑥 𝑦 superscript 𝑒 1 2 𝑥 𝑦 1 4 superscript 𝑦 2 superscript subscript 𝑚 0 superscript 𝑦 𝑚 𝑚 parabolic-V 𝑎 𝑚 𝑥 {\displaystyle{\displaystyle V\left(a,x+y\right)=e^{-\frac{1}{2}xy-\frac{1}{4}% y^{2}}\sum_{m=0}^{\infty}\frac{y^{m}}{m!}V\left(a+m,x\right).}}
    0 references
    DLMF id
    DLMF:12.13.E4
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    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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