DLMF:25.11.E12 (Q7686): Difference between revisions

From DRMF
Jump to navigation Jump to search
Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
(5 intermediate revisions by the same user not shown)
Property / constraint
 

n = 1 , 2 , 3 , 𝑛 1 2 3 {\displaystyle{\displaystyle n=1,2,3,\dots}}

n=1,2,3,\dots
Property / constraint: n = 1 , 2 , 3 , 𝑛 1 2 3 {\displaystyle{\displaystyle n=1,2,3,\dots}} / rank
 
Normal rank
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.m2amdec
Property / Symbols used
 
Property / Symbols used: psi (or digamma) function / rank
 
Normal rank
Property / Symbols used: psi (or digamma) function / qualifier
 
Defining formula:

ψ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}

\digamma@{\NVar{z}}
Property / Symbols used: psi (or digamma) function / qualifier
 
xml-id: C5.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aadec
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.m1hdec
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.m1kdec

Latest revision as of 13:38, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:25.11.E12
No description defined

    Statements

    ζ ( n + 1 , a ) = ( - 1 ) n + 1 ψ ( n ) ( a ) n ! , Hurwitz-zeta 𝑛 1 𝑎 superscript 1 𝑛 1 digamma 𝑛 𝑎 𝑛 {\displaystyle{\displaystyle\zeta\left(n+1,a\right)=\frac{(-1)^{n+1}{\psi^{(n)% }}\left(a\right)}{n!},}}
    0 references
    DLMF:25.11.E12
    0 references
    n = 1 , 2 , 3 , 𝑛 1 2 3 {\displaystyle{\displaystyle n=1,2,3,\dots}}
    0 references
    ζ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    C25.S11.E1.m2amdec
    0 references
    ψ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    C5.S2.E2.m2adec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C25.S1.XMD3.m1hdec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C25.S1.XMD6.m1kdec
    0 references