DLMF:25.11.E4 (Q7678): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Hurwitz zeta function / rank
 
Normal rank
Property / Symbols used: Hurwitz zeta function / qualifier
 
Defining formula:

ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}

\Hurwitzzeta@{\NVar{s}}{\NVar{a}}
Property / Symbols used: Hurwitz zeta function / qualifier
 
xml-id: C25.S11.E1.m2acdec
Property / Symbols used
 
Property / Symbols used: Q12151 / rank
 
Normal rank
Property / Symbols used: Q12151 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12151 / qualifier
 
xml-id: C25.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q12148 / rank
 
Normal rank
Property / Symbols used: Q12148 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12148 / qualifier
 
xml-id: C25.S1.XMD3.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12161 / rank
 
Normal rank
Property / Symbols used: Q12161 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12161 / qualifier
 
xml-id: C25.S1.XMD6.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12149 / rank
 
Normal rank
Property / Symbols used: Q12149 / qualifier
 
Defining formula:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q12149 / qualifier
 
xml-id: C25.S1.XMD7.m1cdec

Latest revision as of 13:36, 2 January 2020

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DLMF:25.11.E4
No description defined

    Statements

    Defining formula
    ζ ⁡ ( s , a ) = ζ ⁡ ( s , a + m ) + ∑ n = 0 m - 1 1 ( n + a ) s , Hurwitz-zeta 𝑠 𝑎 Hurwitz-zeta 𝑠 𝑎 𝑚 superscript subscript 𝑛 0 𝑚 1 1 superscript 𝑛 𝑎 𝑠 {\displaystyle{\displaystyle\zeta\left(s,a\right)=\zeta\left(s,a+m\right)+\sum% _{n=0}^{m-1}\frac{1}{(n+a)^{s}},}}
    0 references
    DLMF id
    DLMF:25.11.E4
    0 references
    constraint
    m = 1 , 2 , 3 , … 𝑚 1 2 3 … {\displaystyle{\displaystyle m=1,2,3,\dots}}
    0 references
    Symbols used
    Hurwitz zeta function
    Defining formula
    ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2acdec
    0 references
    Q12151
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C25.S1.XMD2.m1dec
    0 references
    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1bdec
    0 references
    Q12161
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C25.S1.XMD6.m1bdec
    0 references
    Q12149
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1cdec
    0 references
     
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