DLMF:8.4.E1 (Q2495): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
imported>Admin
 
(2 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

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
 
test:

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
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3adec

Latest revision as of 12:38, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:8.4.E1
No description defined

    Statements

    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
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1adec
    0 references
    erf z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}
    C7.S2.E1.m2adec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    γ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    C8.S2.E1.m2adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3adec
    0 references