DLMF:1.17.E7 (Q666): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2abdec

Revision as of 15:43, 1 January 2020

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DLMF:1.17.E7
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    Statements

    lim n n π - e - n ( x - a ) 2 ϕ ( x ) d x = 1 2 ϕ ( a - ) + 1 2 ϕ ( a + ) . subscript 𝑛 𝑛 𝜋 superscript subscript superscript 𝑒 𝑛 superscript 𝑥 𝑎 2 italic-ϕ 𝑥 𝑥 1 2 italic-ϕ limit-from 𝑎 1 2 italic-ϕ limit-from 𝑎 {\displaystyle{\displaystyle\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty% }^{\infty}e^{-n(x-a)^{2}}\phi(x)\mathrm{d}x=\tfrac{1}{2}\phi(a-)+\tfrac{1}{2}% \phi(a+).}}
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2abdec
    0 references