DLMF:1.17.E6 (Q665)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:1.17.E6
No description defined

    Statements

    Defining formula
    lim n → ∞ ⁡ n π ⁢ ∫ - ∞ ∞ e - n ⁢ ( x - a ) 2 ⁢ ϕ ⁢ ( x ) ⁢ d x = ϕ ⁢ ( a ) , subscript → 𝑛 𝑛 𝜋 superscript subscript superscript 𝑒 𝑛 superscript 𝑥 𝑎 2 italic-ϕ 𝑥 𝑥 italic-ϕ 𝑎 {\displaystyle{\displaystyle\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty% }^{\infty}e^{-n(x-a)^{2}}\phi(x)\mathrm{d}x=\phi(a),}}
    0 references
    DLMF id
    DLMF:1.17.E6
    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.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1cdec
    0 references
    Q10916
    Defining formula
    ϕ ⁢ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}
    xml-id
    C1.S17.XMD1.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q665&oldid=23846"