DLMF:8.4.E3 (Q2497): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(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
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec
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-star 𝑎 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}

\scincgamma@{\NVar{a}}{\NVar{z}}
Property / Symbols used: incomplete gamma function / qualifier
 
xml-id: C8.S2.E6.m2aadec
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.m1adec

Latest revision as of 13:38, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:8.4.E3
No description defined

    Statements

    γ * ( 1 2 , - z 2 ) = 2 e z 2 z π F ( z ) . incomplete-gamma-star 1 2 superscript 𝑧 2 2 superscript 𝑒 superscript 𝑧 2 𝑧 𝜋 Dawsons-integral 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\tfrac{1}{2},-z^{2}\right)=\frac{2% e^{z^{2}}}{z\sqrt{\pi}}F\left(z\right).}}
    0 references
    DLMF:8.4.E3
    0 references
    F ( z ) Dawsons-integral 𝑧 {\displaystyle{\displaystyle F\left(\NVar{z}\right)}}
    C7.S2.E5.m2adec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aadec
    0 references
    γ * ( a , z ) incomplete-gamma-star 𝑎 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}
    C8.S2.E6.m2aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C8.S1.XMD2.m1adec
    0 references