DLMF:25.6.E12 (Q7649): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(3 intermediate revisions by the same user not shown)
Property / testProperty / test

ζ ′′ ⁡ ( 0 ) = - 1 2 ⁢ ( ln ⁡ ( 2 ⁢ π ) ) 2 + 1 2 ⁢ γ 2 - 1 24 ⁢ π 2 + γ 1 , diffop Riemann-zeta 2 0 1 2 superscript 2 𝜋 2 1 2 2 1 24 superscript 𝜋 2 Stieltjes-constants 1 {\displaystyle{\displaystyle\zeta''\left(0\right)=-\tfrac{1}{2}(\ln\left(2\pi% \right))^{2}+\tfrac{1}{2}{\gamma^{2}}-\tfrac{1}{24}\pi^{2}+\gamma_{1},}}

\Riemannzeta''@{0}=-\tfrac{1}{2}(\ln@{2\pi})^{2}+\tfrac{1}{2}\EulerConstant^{2}-\tfrac{1}{24}\pi^{2}+\StieltjesConstants{1},

ζ ′′ ⁡ ( 0 ) = - 1 2 ⁢ ( ln ⁡ ( 2 ⁢ π ) ) 2 + 1 2 ⁢ γ 2 - 1 24 ⁢ π 2 + γ 1 diffop Riemann-zeta 2 0 1 2 superscript 2 𝜋 2 1 2 2 1 24 superscript 𝜋 2 Stieltjes-constants 1 {\displaystyle{\displaystyle\zeta''\left(0\right)=-\tfrac{1}{2}(\ln\left(2\pi% \right))^{2}+\tfrac{1}{2}{\gamma^{2}}-\tfrac{1}{24}\pi^{2}+\gamma_{1}}}

\Riemannzeta''@{0}=-\tfrac{1}{2}(\ln@{2\pi})^{2}+\tfrac{1}{2}\EulerConstant^{2}-\tfrac{1}{24}\pi^{2}+\StieltjesConstants{1}
Property / Symbols used
 
Property / Symbols used: Stieltjes constants / rank
 
Normal rank
Property / Symbols used: Stieltjes constants / qualifier
 
test:

γ n Stieltjes-constants 𝑛 {\displaystyle{\displaystyle\gamma_{\NVar{n}}}}

\StieltjesConstants{\NVar{n}}
Property / Symbols used: Stieltjes constants / qualifier
 
xml-id: C25.S2.E5.m2adec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2addec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aadec

Latest revision as of 15:07, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:25.6.E12
No description defined

    Statements

    test
    ζ ′′ ⁡ ( 0 ) = - 1 2 ⁢ ( ln ⁡ ( 2 ⁢ π ) ) 2 + 1 2 ⁢ γ 2 - 1 24 ⁢ π 2 + γ 1 diffop Riemann-zeta 2 0 1 2 superscript 2 𝜋 2 1 2 2 1 24 superscript 𝜋 2 Stieltjes-constants 1 {\displaystyle{\displaystyle\zeta''\left(0\right)=-\tfrac{1}{2}(\ln\left(2\pi% \right))^{2}+\tfrac{1}{2}{\gamma^{2}}-\tfrac{1}{24}\pi^{2}+\gamma_{1}}}
    0 references
    DLMF id
    DLMF:25.6.E12
    0 references
    Symbols used
    Euler’s constant
    test
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
    Riemann zeta function
    test
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2akdec
    0 references
    Stieltjes constants
    test
    γ n Stieltjes-constants 𝑛 {\displaystyle{\displaystyle\gamma_{\NVar{n}}}}
    xml-id
    C25.S2.E5.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q7649&oldid=42928"