DLMF:8.10.E11 (Q2568): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2agdec
Property / Symbols used
 
Property / Symbols used: Q11325 / rank
 
Normal rank
Property / Symbols used: Q11325 / qualifier
 
test:

P ⁡ ( a , z ) incomplete-gamma-P 𝑎 𝑧 {\displaystyle{\displaystyle P\left(\NVar{a},\NVar{z}\right)}}

\normincGammaP@{\NVar{a}}{\NVar{z}}
Property / Symbols used: Q11325 / qualifier
 
xml-id: C8.S2.E4.m1adec
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.m1idec
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.m1jdec
Property / Symbols used
 
Property / Symbols used: Q11340 / rank
 
Normal rank
Property / Symbols used: Q11340 / qualifier
 
test:

α a subscript 𝛼 𝑎 {\displaystyle{\displaystyle\alpha_{a}}}

\alpha_{a}
Property / Symbols used: Q11340 / qualifier
 
xml-id: C8.S10.XMD7.m1dec
Property / Symbols used
 
Property / Symbols used: Q11341 / rank
 
Normal rank
Property / Symbols used: Q11341 / qualifier
 
test:

β a subscript 𝛽 𝑎 {\displaystyle{\displaystyle\beta_{a}}}

\beta_{a}
Property / Symbols used: Q11341 / qualifier
 
xml-id: C8.S10.XMD8.m1dec

Latest revision as of 12:52, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:8.10.E11
No description defined

    Statements

    test
    ( 1 - e - α a ⁢ x ) a ≤ P ⁡ ( a , x ) ≤ ( 1 - e - β a ⁢ x ) a , superscript 1 superscript 𝑒 subscript 𝛼 𝑎 𝑥 𝑎 incomplete-gamma-P 𝑎 𝑥 superscript 1 superscript 𝑒 subscript 𝛽 𝑎 𝑥 𝑎 {\displaystyle{\displaystyle(1-e^{-\alpha_{a}x})^{a}\leq P\left(a,x\right)\leq% (1-e^{-\beta_{a}x})^{a},}}
    0 references
    DLMF id
    DLMF:8.10.E11
    0 references
    constraint
    a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}}
    0 references
    Symbols used
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2agdec
    0 references
    Q11325
    test
    P ⁡ ( a , z ) incomplete-gamma-P 𝑎 𝑧 {\displaystyle{\displaystyle P\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E4.m1adec
    0 references
    Q11332
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1idec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1jdec
    0 references
    Q11340
    test
    α a subscript 𝛼 𝑎 {\displaystyle{\displaystyle\alpha_{a}}}
    xml-id
    C8.S10.XMD7.m1dec
    0 references
    Q11341
    test
    β a subscript 𝛽 𝑎 {\displaystyle{\displaystyle\beta_{a}}}
    xml-id
    C8.S10.XMD8.m1dec
    0 references
     
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