DLMF:8.10.E5 (Q2558): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(5 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
 
Defining formula:

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.m2abdec
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.m1ddec
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.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11329 / rank
 
Normal rank
Property / Symbols used: Q11329 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11329 / qualifier
 
xml-id: C8.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q11336 / rank
 
Normal rank
Property / Symbols used: Q11336 / qualifier
 
Defining formula:

A n subscript 𝐴 𝑛 {\displaystyle{\displaystyle A_{n}}}

A_{n}
Property / Symbols used: Q11336 / qualifier
 
xml-id: C8.S10.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q11337 / rank
 
Normal rank
Property / Symbols used: Q11337 / qualifier
 
Defining formula:

B n subscript 𝐵 𝑛 {\displaystyle{\displaystyle B_{n}}}

B_{n}
Property / Symbols used: Q11337 / qualifier
 
xml-id: C8.S10.XMD3.m1dec

Latest revision as of 13:51, 2 January 2020

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DLMF:8.10.E5
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    Statements

    A n < x 1 - a e x Γ ( a , x ) < B n , subscript 𝐴 𝑛 superscript 𝑥 1 𝑎 superscript 𝑒 𝑥 incomplete-Gamma 𝑎 𝑥 subscript 𝐵 𝑛 {\displaystyle{\displaystyle A_{n}<x^{1-a}e^{x}\Gamma\left(a,x\right)<B_{n},}}
    0 references
    DLMF:8.10.E5
    0 references
    a < 1 𝑎 1 {\displaystyle{\displaystyle a<1}}
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2acdec
    0 references
    Γ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    C8.S2.E2.m2abdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C8.S1.XMD1.m1ddec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C8.S1.XMD3.m1ddec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C8.S1.XMD6.m1dec
    0 references
    A n subscript 𝐴 𝑛 {\displaystyle{\displaystyle A_{n}}}
    C8.S10.XMD2.m1dec
    0 references
    B n subscript 𝐵 𝑛 {\displaystyle{\displaystyle B_{n}}}
    C8.S10.XMD3.m1dec
    0 references