DLMF:8.8.E4 (Q2536): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 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.m2abdec
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.m2adec
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.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1cdec

Latest revision as of 13:47, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:8.8.E4
No description defined

    Statements

    z γ * ( a + 1 , z ) = γ * ( a , z ) - e - z Γ ( a + 1 ) . 𝑧 incomplete-gamma-star 𝑎 1 𝑧 incomplete-gamma-star 𝑎 𝑧 superscript 𝑒 𝑧 Euler-Gamma 𝑎 1 {\displaystyle{\displaystyle z\gamma^{*}\left(a+1,z\right)=\gamma^{*}\left(a,z% \right)-\frac{e^{-z}}{\Gamma\left(a+1\right)}.}}
    0 references
    DLMF:8.8.E4
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2adec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2abdec
    0 references
    γ * ( a , z ) incomplete-gamma-star 𝑎 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}
    C8.S2.E6.m2adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C8.S1.XMD2.m1cdec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C8.S1.XMD3.m1cdec
    0 references