DLMF:8.14.E1 (Q2634): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(One intermediate revision by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11332 / rank
 
Normal rank
Property / Symbols used: Q11332 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11332 / qualifier
 
xml-id: C8.S1.XMD1.m1dec
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.m1dec

Latest revision as of 14:00, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:8.14.E1
No description defined

    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ x ⁢ γ ⁡ ( b , x ) Γ ⁡ ( b ) ⁢ d x = ( 1 + a ) - b a , superscript subscript 0 superscript 𝑒 𝑎 𝑥 incomplete-gamma 𝑏 𝑥 Euler-Gamma 𝑏 𝑥 superscript 1 𝑎 𝑏 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-ax}\frac{\gamma\left(b,x% \right)}{\Gamma\left(b\right)}\mathrm{d}x=\frac{(1+a)^{-b}}{a},}}
    0 references
    DLMF id
    DLMF:8.14.E1
    0 references
    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    ℜ ⁡ b > - 1 𝑏 1 {\displaystyle{\displaystyle\Re b>-1}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    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
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    Q11332
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1dec
    0 references
    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2634&oldid=42378"