DLMF:7.7.E5 (Q2375): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3addec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1abdec

Latest revision as of 01:44, 2 January 2020

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DLMF:7.7.E5
No description defined

    Statements

    Defining formula
    ∫ 0 1 e - a ⁢ t 2 t 2 + 1 ⁢ d t = π 4 ⁢ e a ⁢ ( 1 - ( erf ⁡ a ) 2 ) , superscript subscript 0 1 superscript 𝑒 𝑎 superscript 𝑡 2 superscript 𝑡 2 1 𝑡 𝜋 4 superscript 𝑒 𝑎 1 superscript error-function 𝑎 2 {\displaystyle{\displaystyle\int_{0}^{1}\frac{e^{-at^{2}}}{t^{2}+1}\mathrm{d}t% =\frac{\pi}{4}e^{a}\left(1-(\operatorname{erf}\sqrt{a})^{2}\right),}}
    0 references
    DLMF id
    DLMF:7.7.E5
    0 references
    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    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.m2addec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    error function
    Defining formula
    erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}
    xml-id
    C7.S2.E1.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
     
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