DLMF:8.22.E1 (Q2750): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(6 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2adec
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
 
test:

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: generalized exponential integral / rank
 
Normal rank
Property / Symbols used: generalized exponential integral / qualifier
 
test:

E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}

\genexpintE{\NVar{p}}@{\NVar{z}}
Property / Symbols used: generalized exponential integral / qualifier
 
xml-id: C8.S19.E1.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.E2.m2adec
Property / Symbols used
 
Property / Symbols used: terminant function / rank
 
Normal rank
Property / Symbols used: terminant function / qualifier
 
test:

F p ⁡ ( z ) terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle F_{\NVar{p}}\left(\NVar{z}\right)}}

\terminant{\NVar{p}}@{\NVar{z}}
Property / Symbols used: terminant function / qualifier
 
xml-id: C2.S11.E11.m2adec
Property / Symbols used
 
Property / Symbols used: Q11323 / rank
 
Normal rank
Property / Symbols used: Q11323 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11323 / qualifier
 
xml-id: C8.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q11377 / rank
 
Normal rank
Property / Symbols used: Q11377 / qualifier
 
test:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q11377 / qualifier
 
xml-id: C8.S1.XMD4.m1dec

Latest revision as of 13:20, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:8.22.E1
No description defined

    Statements

    test
    F p ⁡ ( z ) = Γ ⁡ ( p ) 2 ⁢ π ⁢ z 1 - p ⁢ E p ⁡ ( z ) = Γ ⁡ ( p ) 2 ⁢ π ⁢ Γ ⁡ ( 1 - p , z ) , terminant-function 𝑝 𝑧 Euler-Gamma 𝑝 2 𝜋 superscript 𝑧 1 𝑝 exponential-integral-En 𝑝 𝑧 Euler-Gamma 𝑝 2 𝜋 incomplete-Gamma 1 𝑝 𝑧 {\displaystyle{\displaystyle F_{p}\left(z\right)=\frac{\Gamma\left(p\right)}{2% \pi}z^{1-p}E_{p}\left(z\right)=\frac{\Gamma\left(p\right)}{2\pi}\Gamma\left(1-% p,z\right),}}
    0 references
    DLMF id
    DLMF:8.22.E1
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    generalized exponential integral
    test
    E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C8.S19.E1.m2adec
    0 references
    incomplete gamma function
    test
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2adec
    0 references
    terminant function
    test
    F p ⁡ ( z ) terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle F_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C2.S11.E11.m2adec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1dec
    0 references
    Q11377
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C8.S1.XMD4.m1dec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2750&oldid=14077"