DLMF:8.10.E10 (Q2567): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(3 intermediate revisions by the same user not shown)
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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11332 / rank
 
Normal rank
Property / Symbols used: Q11332 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11332 / qualifier
 
xml-id: C8.S1.XMD1.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1idec
Property / Symbols used
 
Property / Symbols used: Q11339 / rank
 
Normal rank
Property / Symbols used: Q11339 / qualifier
 
test:

c a subscript 𝑐 𝑎 {\displaystyle{\displaystyle c_{a}}}

c_{a}
Property / Symbols used: Q11339 / qualifier
 
xml-id: C8.S10.XMD5.m1adec

Latest revision as of 12:52, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:8.10.E10
No description defined

    Statements

    test
    x 2 ⁢ a ⁢ ( ( 1 + 2 x ) a - 1 ) < x 1 - a ⁢ e x ⁢ Γ ⁡ ( a , x ) ≤ x a ⁢ c a ⁢ ( ( 1 + c a x ) a - 1 ) , 𝑥 2 𝑎 superscript 1 2 𝑥 𝑎 1 superscript 𝑥 1 𝑎 superscript 𝑒 𝑥 incomplete-Gamma 𝑎 𝑥 𝑥 𝑎 subscript 𝑐 𝑎 superscript 1 subscript 𝑐 𝑎 𝑥 𝑎 1 {\displaystyle{\displaystyle\frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1% \right)<x^{1-a}e^{x}\Gamma\left(a,x\right)\leq\frac{x}{ac_{a}}\left(\left(1+% \frac{c_{a}}{x}\right)^{a}-1\right),}}
    0 references
    DLMF id
    DLMF:8.10.E10
    0 references
    constraint
    0 < a < 1 0 𝑎 1 {\displaystyle{\displaystyle 0<a<1}}
    0 references
    Symbols used
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    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.m2acdec
    0 references
    Q11332
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1hdec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1idec
    0 references
    Q11339
    test
    c a subscript 𝑐 𝑎 {\displaystyle{\displaystyle c_{a}}}
    xml-id
    C8.S10.XMD5.m1adec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2567&oldid=12956"