DLMF:8.4.E1 (Q2495): 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
 
Defining formula:

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.m2adec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1adec
Property / Symbols used
 
Property / Symbols used: error function / rank
 
Normal rank
Property / Symbols used: error function / qualifier
 
Defining formula:

erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}

\erf@@{\NVar{z}}
Property / Symbols used: error function / qualifier
 
xml-id: C7.S2.E1.m2adec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
Property / Symbols used
 
Property / Symbols used: incomplete gamma function / rank
 
Normal rank
Property / Symbols used: incomplete gamma function / qualifier
 
Defining formula:

γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}

\incgamma@{\NVar{a}}{\NVar{z}}
Property / Symbols used: incomplete gamma function / qualifier
 
xml-id: C8.S2.E1.m2adec
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.m3adec
Property / Symbols used
 
Property / Symbols used: Q11323 / rank
 
Normal rank
Property / Symbols used: Q11323 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11323 / qualifier
 
xml-id: C8.S1.XMD2.m1dec

Latest revision as of 13:38, 2 January 2020

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DLMF:8.4.E1
No description defined

    Statements

    Defining formula
    γ ⁡ ( 1 2 , z 2 ) = 2 ⁢ ∫ 0 z e - t 2 ⁢ d t = π ⁢ erf ⁡ ( z ) , incomplete-gamma 1 2 superscript 𝑧 2 2 superscript subscript 0 𝑧 superscript 𝑒 superscript 𝑡 2 𝑡 𝜋 error-function 𝑧 {\displaystyle{\displaystyle\gamma\left(\tfrac{1}{2},z^{2}\right)=2\int_{0}^{z% }e^{-t^{2}}\mathrm{d}t=\sqrt{\pi}\operatorname{erf}\left(z\right),}}
    0 references
    DLMF id
    DLMF:8.4.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
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    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.m2adec
    0 references
    incomplete gamma function
    Defining formula
    γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E1.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1dec
    0 references
     
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