DLMF:7.20.E1 (Q2479): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11322 / rank
 
Normal rank
Property / Symbols used: Q11322 / qualifier
 
Defining formula:

σ 𝜎 {\displaystyle{\displaystyle\sigma}}

\sigma
Property / Symbols used: Q11322 / qualifier
 
xml-id: C7.S20.XMD2.m1dec

Latest revision as of 13:35, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:7.20.E1
No description defined

    Statements

    Defining formula
    1 σ ⁢ 2 ⁢ π ⁢ ∫ - ∞ x e - ( t - m ) 2 / ( 2 ⁢ σ 2 ) ⁢ d t = 1 2 ⁢ erfc ⁡ ( m - x σ ⁢ 2 ) = Q ⁢ ( m - x σ ) = P ⁢ ( x - m σ ) . 1 𝜎 2 𝜋 superscript subscript 𝑥 superscript 𝑒 superscript 𝑡 𝑚 2 2 superscript 𝜎 2 𝑡 1 2 complementary-error-function 𝑚 𝑥 𝜎 2 𝑄 𝑚 𝑥 𝜎 𝑃 𝑥 𝑚 𝜎 {\displaystyle{\displaystyle\frac{1}{\sigma\sqrt{2\pi}}\int_{-\infty}^{x}e^{-(% t-m)^{2}/(2\sigma^{2})}\mathrm{d}t=\frac{1}{2}\operatorname{erfc}\left(\frac{m% -x}{\sigma\sqrt{2}}\right)=Q\left(\frac{m-x}{\sigma}\right)=P\left(\frac{x-m}{% \sigma}\right).}}
    0 references
    DLMF id
    DLMF:7.20.E1
    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.m2adec
    0 references
    complementary error function
    Defining formula
    erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    xml-id
    C7.S2.E2.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11313
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C7.S1.XMD1.m1dec
    0 references
    Q11321
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C7.S20.XMD1.m1dec
    0 references
    Q11322
    Defining formula
    σ 𝜎 {\displaystyle{\displaystyle\sigma}}
    xml-id
    C7.S20.XMD2.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2479&oldid=37954"