DLMF:12.13.E2 (Q4231)

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DLMF:12.13.E2
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    Statements

    Defining formula
    U ⁡ ( a , x + y ) = e - 1 2 ⁢ x ⁢ y - 1 4 ⁢ y 2 ⁢ ∑ m = 0 ∞ ( - a - 1 2 m ) ⁢ y 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 binomial 𝑎 1 2 𝑚 superscript 𝑦 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}\genfrac{(}{)}{0.0pt}{}{-a-\tfrac{1}{2}}{m}y^{m}U% \left(a+m,x\right),}}
    0 references
    DLMF id
    DLMF:12.13.E2
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    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.m1aadec
    0 references
    Q11520
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C12.S1.XMD1.m1adec
    0 references
    Q11542
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C12.S1.XMD2.m1adec
    0 references
    Q11516
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1adec
    0 references
     
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