DLMF:25.11.E10 (Q7684): Difference between revisions

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imported>Admin
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Property / constraint
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| a - 1 | < 1 π‘Ž 1 1 {\displaystyle{\displaystyle|a-1|<1}}

|a-1|<1
Property / constraint: | a - 1 | < 1 π‘Ž 1 1 {\displaystyle{\displaystyle|a-1|<1}} / rank
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Normal rank
Property / Symbols used
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Property / Symbols used: gamma function / rank
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Normal rank
Property / Symbols used: gamma function / qualifier
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test:

Ξ“ ⁑ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

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

ΞΆ ⁑ ( s , a ) Hurwitz-zeta 𝑠 π‘Ž {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}

\Hurwitzzeta@{\NVar{s}}{\NVar{a}}
Property / Symbols used: Hurwitz zeta function / qualifier
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xml-id: C25.S11.E1.m2akdec
Property / Symbols used
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Property / Symbols used: Q10759 / rank
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Normal rank
Property / Symbols used: Q10759 / qualifier
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test:

( a ) n Pochhammer π‘Ž 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
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xml-id: C5.S2.SS3.m1adec
Property / Symbols used
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Property / Symbols used: Riemann zeta function / rank
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Normal rank
Property / Symbols used: Riemann zeta function / qualifier
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test:

ΞΆ ⁑ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}

\Riemannzeta@{\NVar{s}}
Property / Symbols used: Riemann zeta function / qualifier
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xml-id: C25.S2.E1.m2aadec
Property / Symbols used
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Property / Symbols used: Q10755 / rank
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Normal rank
Property / Symbols used: Q10755 / qualifier
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test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
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xml-id: introduction.Sx4.p1.t1.r15.m5adec
Property / Symbols used
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Property / Symbols used: Q12148 / rank
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Normal rank
Property / Symbols used: Q12148 / qualifier
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test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12148 / qualifier
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xml-id: C25.S1.XMD3.m1gdec
Property / Symbols used
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Property / Symbols used: Q12161 / rank
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Normal rank
Property / Symbols used: Q12161 / qualifier
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test:

a π‘Ž {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12161 / qualifier
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xml-id: C25.S1.XMD6.m1jdec
Property / Symbols used
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Property / Symbols used: Q12149 / rank
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Normal rank
Property / Symbols used: Q12149 / qualifier
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test:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q12149 / qualifier
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xml-id: C25.S1.XMD7.m1idec
Property / Symbols used
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Property / Symbols used: Q12156 / rank
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Normal rank
Property / Symbols used: Q12156 / qualifier
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test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12156 / qualifier
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xml-id: C25.S1.XMD8.m1dec

Latest revision as of 12:38, 2 January 2020

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DLMF:25.11.E10
No description defined

    Statements

    test
    ΞΆ ⁑ ( s , a ) = βˆ‘ n = 0 ∞ ( s ) n n ! ⁒ ΞΆ ⁑ ( n + s ) ⁒ ( 1 - a ) n , Hurwitz-zeta 𝑠 π‘Ž superscript subscript 𝑛 0 Pochhammer 𝑠 𝑛 𝑛 Riemann-zeta 𝑛 𝑠 superscript 1 π‘Ž 𝑛 {\displaystyle{\displaystyle\zeta\left(s,a\right)=\sum_{n=0}^{\infty}\frac{{% \left(s\right)_{n}}}{n!}\zeta\left(n+s\right)(1-a)^{n},}}
    0 references
    DLMF id
    DLMF:25.11.E10
    0 references
    constraint
    | a - 1 | < 1 π‘Ž 1 1 {\displaystyle{\displaystyle|a-1|<1}}
    0 references
    Symbols used
    gamma function
    test
    Ξ“ ⁑ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Hurwitz zeta function
    test
    ΞΆ ⁑ ( s , a ) Hurwitz-zeta 𝑠 π‘Ž {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2akdec
    0 references
    Q10759
    test
    ( a ) n Pochhammer π‘Ž 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Riemann zeta function
    test
    ΞΆ ⁑ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aadec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q12148
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1gdec
    0 references
    Q12161
    test
    a π‘Ž {\displaystyle{\displaystyle a}}
    xml-id
    C25.S1.XMD6.m1jdec
    0 references
    Q12149
    test
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1idec
    0 references
    Q12156
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C25.S1.XMD8.m1dec
    0 references
     
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