DLMF:1.15.E37 (Q579)

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DLMF:1.15.E37
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    Statements

    Defining formula
    h ⁢ ( x , y ) = 1 2 ⁢ π ⁢ ∫ - ∞ ∞ f ⁢ ( t ) ⁢ P ⁢ ( x - t , y ) ⁢ d t ℎ 𝑥 𝑦 1 2 𝜋 subscript superscript 𝑓 𝑡 𝑃 𝑥 𝑡 𝑦 𝑡 {\displaystyle{\displaystyle h(x,y)=\frac{1}{2\pi}\int^{\infty}_{-\infty}f(t)P% (x-t,y)\mathrm{d}t}}
    0 references
    DLMF id
    DLMF:1.15.E37
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aldec
    0 references
    Poisson kernel (locally)
    Defining formula
    P ⁢ ( x , y ) 𝑃 𝑥 𝑦 {\displaystyle{\displaystyle P(x,y)}}
    xml-id
    C1.S15.XMD7.m1cdec
    0 references
    Q10899
    Defining formula
    h ⁢ ( x , y ) ℎ 𝑥 𝑦 {\displaystyle{\displaystyle h(x,y)}}
    xml-id
    C1.S15.XMD8.m1adec
    0 references
     
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