DLMF:8.10.E10 (Q2567)

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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}}
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    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
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    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1idec
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    Q11339
    test
    c a subscript 𝑐 𝑎 {\displaystyle{\displaystyle c_{a}}}
    xml-id
    C8.S10.XMD5.m1adec
    0 references
     
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