DLMF:5.6.E4 (Q2071)

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DLMF:5.6.E4
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    Statements

    test
    x 1 - s < Γ ⁡ ( x + 1 ) Γ ⁡ ( x + s ) < ( x + 1 ) 1 - s , superscript 𝑥 1 𝑠 Euler-Gamma 𝑥 1 Euler-Gamma 𝑥 𝑠 superscript 𝑥 1 1 𝑠 {\displaystyle{\displaystyle x^{1-s}<\frac{\Gamma\left(x+1\right)}{\Gamma\left% (x+s\right)}<(x+1)^{1-s},}}
    0 references
    DLMF id
    DLMF:5.6.E4
    0 references
    constraint
    0 < s < 1 0 𝑠 1 {\displaystyle{\displaystyle 0<s<1}}
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    Q11282
    test
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C5.S1.XMD11.m1dec
    0 references
    Q11281
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C5.S1.XMD5.m1cdec
    0 references
     
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