DLMF:25.16.E11 (Q7767): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
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Property / constraint
 

( s + z ) > 1 𝑠 𝑧 1 {\displaystyle{\displaystyle\Re(s+z)>1}}

\realpart@@{(s+z)}>1
Property / constraint: ( s + z ) > 1 𝑠 𝑧 1 {\displaystyle{\displaystyle\Re(s+z)>1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q12170 / rank
 
Normal rank
Property / Symbols used: Q12170 / qualifier
 
Defining formula:

H ( s , z ) generalized-Euler-sum-H 𝑠 𝑧 {\displaystyle{\displaystyle H\left(\NVar{s},\NVar{z}\right)}}

\genEulersumH@{\NVar{s}}{\NVar{z}}
Property / Symbols used: Q12170 / qualifier
 
xml-id: C25.S16.SS2.p7.m3adec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
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.m1adec
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.m1cdec
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
Property / Symbols used
 
Property / Symbols used: Q12156 / rank
 
Normal rank
Property / Symbols used: Q12156 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

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

Latest revision as of 01:07, 2 January 2020

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DLMF:25.16.E11
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    Statements

    H ( s , z ) = n = 1 1 n s m = 1 n 1 m z , generalized-Euler-sum-H 𝑠 𝑧 superscript subscript 𝑛 1 1 superscript 𝑛 𝑠 superscript subscript 𝑚 1 𝑛 1 superscript 𝑚 𝑧 {\displaystyle{\displaystyle H\left(s,z\right)=\sum_{n=1}^{\infty}\frac{1}{n^{% s}}\sum_{m=1}^{n}\frac{1}{m^{z}},}}
    0 references
    DLMF:25.16.E11
    0 references
    ( s + z ) > 1 𝑠 𝑧 1 {\displaystyle{\displaystyle\Re(s+z)>1}}
    0 references
    H ( s , z ) generalized-Euler-sum-H 𝑠 𝑧 {\displaystyle{\displaystyle H\left(\NVar{s},\NVar{z}\right)}}
    C25.S16.SS2.p7.m3adec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
    0 references
    m 𝑚 {\displaystyle{\displaystyle m}}
    C25.S1.XMD2.m1adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C25.S1.XMD3.m1cdec
    0 references
    s 𝑠 {\displaystyle{\displaystyle s}}
    C25.S1.XMD7.m1cdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C25.S1.XMD8.m1dec
    0 references