DLMF:8.22.E2 (Q2751): Difference between revisions

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Property / constraint
 

s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}

\realpart@@{s}>1
Property / constraint: s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3adec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.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.m1dec

Latest revision as of 13:20, 2 January 2020

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DLMF:8.22.E2
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    Statements

    ζ x ( s ) = 1 Γ ( s ) 0 x t s - 1 e t - 1 d t , subscript 𝜁 𝑥 𝑠 1 Euler-Gamma 𝑠 superscript subscript 0 𝑥 superscript 𝑡 𝑠 1 superscript 𝑒 𝑡 1 𝑡 {\displaystyle{\displaystyle\zeta_{x}(s)=\frac{1}{\Gamma\left(s\right)}\int_{0% }^{x}\frac{t^{s-1}}{e^{t}-1}\mathrm{d}t,}}
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    s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aadec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1adec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3adec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C8.S1.XMD1.m1dec
    0 references