@@ Property / constraint @@
+ ${\displaystyle{\displaystyle|\ln z|<2\pi}}$ 
|\ln@@{z}|<2\pi
@@ Property / constraint: ${\displaystyle{\displaystyle|\ln z|<2\pi}}$ / rank @@
+Normal rank
@@ Property / constraint @@
+ ${\displaystyle{\displaystyle s\neq 1,2,3,\dots}}$ 
s\neq 1,2,3,\dots
+Normal rank
@@ Property / constraint @@
+ ${\displaystyle{\displaystyle|\ln z|<2\pi}}$ 
|\ln z|<2\pi
@@ Property / constraint: ${\displaystyle{\displaystyle|\ln z|<2\pi}}$ / rank @@
+Normal rank
@@ Property / Symbols used @@
+gamma function
@@ Property / Symbols used: gamma function / rank @@
+Normal rank
@@ Property / Symbols used: gamma function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ 
\EulerGamma@{\NVar{z}}
@@ Property / Symbols used: gamma function / qualifier @@
+xml-id: C5.S2.E1.m2aadec
@@ Property / Symbols used @@
+Riemann zeta function
@@ Property / Symbols used: Riemann zeta function / rank @@
+Normal rank
@@ Property / Symbols used: Riemann zeta function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$ 
\Riemannzeta@{\NVar{s}}
@@ Property / Symbols used: Riemann zeta function / qualifier @@
+xml-id: C25.S2.E1.m2adec
@@ Property / Symbols used @@
+the ratio of the circumference of a circle to its diameter
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle\pi}}$ 
\cpi
+xml-id: C3.S12.E1.m2addec
@@ Property / Symbols used @@
+Q10755
@@ 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.m5adec
@@ Property / Symbols used @@
+principal branch of logarithm function
@@ Property / Symbols used: principal branch of logarithm function / rank @@
+Normal rank
@@ Property / Symbols used: principal branch of logarithm function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\ln\NVar{z}}}$ 
\ln@@{\NVar{z}}
@@ Property / Symbols used: principal branch of logarithm function / qualifier @@
+xml-id: C4.S2.E2.m2aedec
@@ Property / Symbols used @@
+polylogarithm
@@ Property / Symbols used: polylogarithm / rank @@
+Normal rank
@@ Property / Symbols used: polylogarithm / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{Li}_{\NVar{s}}\left(\NVar{z}\right)}}$ 
\polylog{\NVar{s}}@{\NVar{z}}
@@ Property / Symbols used: polylogarithm / qualifier @@
+xml-id: C25.S12.E10.m2abdec
@@ Property / Symbols used @@
+Q12148
@@ Property / Symbols used: Q12148 / rank @@
+Normal rank
@@ Property / Symbols used: Q12148 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle n}}$ 
n
@@ Property / Symbols used: Q12148 / qualifier @@
+xml-id: C25.S1.XMD3.m1edec
@@ Property / Symbols used @@
+Q12149
@@ Property / Symbols used: Q12149 / rank @@
+Normal rank
@@ Property / Symbols used: Q12149 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle s}}$ 
s
@@ Property / Symbols used: Q12149 / qualifier @@
+xml-id: C25.S1.XMD7.m1bdec
@@ Property / Symbols used @@
+Q12156
@@ Property / Symbols used: Q12156 / rank @@
+Normal rank
@@ Property / Symbols used: Q12156 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle z}}$ 
z
@@ Property / Symbols used: Q12156 / qualifier @@
+xml-id: C25.S1.XMD8.m1gdec

DLMF:25.12.E12 (Q7731): Difference between revisions

| ln ⁡ z | < 2 ⁢ π 𝑧 2 𝜋 {\displaystyle{\displaystyle|\ln z|<2\pi}}

s ≠ 1 , 2 , 3 , … 𝑠 1 2 3 … {\displaystyle{\displaystyle s\neq 1,2,3,\dots}}

| ln ⁡ z | < 2 ⁢ π 𝑧 2 𝜋 {\displaystyle{\displaystyle|\ln z|<2\pi}}

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}

π {\displaystyle{\displaystyle\pi}}

! {\displaystyle{\displaystyle!}}

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

Li s ⁡ ( z ) polylogarithm 𝑠 𝑧 {\displaystyle{\displaystyle\mathrm{Li}_{\NVar{s}}\left(\NVar{z}\right)}}

n 𝑛 {\displaystyle{\displaystyle n}}

s 𝑠 {\displaystyle{\displaystyle s}}

z 𝑧 {\displaystyle{\displaystyle z}}

Latest revision as of 13:49, 2 January 2020

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${\displaystyle{\displaystyle|\ln z|<2\pi}}$

${\displaystyle{\displaystyle s\neq 1,2,3,\dots}}$

${\displaystyle{\displaystyle|\ln z|<2\pi}}$

${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$

${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$

${\displaystyle{\displaystyle\pi}}$

${\displaystyle{\displaystyle!}}$

${\displaystyle{\displaystyle\ln\NVar{z}}}$

${\displaystyle{\displaystyle\mathrm{Li}_{\NVar{s}}\left(\NVar{z}\right)}}$

${\displaystyle{\displaystyle n}}$

${\displaystyle{\displaystyle s}}$

${\displaystyle{\displaystyle z}}$