@@ Property / constraint @@
+ ${\displaystyle{\displaystyle\Re s>1}}$ 
\Re s>1
@@ Property / constraint: ${\displaystyle{\displaystyle\Re s>1}}$ / rank @@
+Normal rank
@@ Property / constraint @@
+ ${\displaystyle{\displaystyle|z|=1,\Re a>0}}$ 
|z|=1,\Re a>0
@@ Property / constraint: ${\displaystyle{\displaystyle|z|=1,\Re a>0}}$ / rank @@
+Normal rank
@@ Property / Symbols used @@
+Lerch’s transcendent
@@ Property / Symbols used: Lerch’s transcendent / rank @@
+Normal rank
@@ Property / Symbols used: Lerch’s transcendent / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)}}$ 
\LerchPhi@{\NVar{z}}{\NVar{s}}{\NVar{a}}
@@ Property / Symbols used: Lerch’s transcendent / qualifier @@
+xml-id: C25.S14.E1.m2aedec
@@ 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.m2adec
@@ Property / Symbols used @@
+Q10770
@@ Property / Symbols used: Q10770 / rank @@
+Normal rank
@@ Property / Symbols used: Q10770 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ 
\diff{\NVar{x}}
@@ Property / Symbols used: Q10770 / qualifier @@
+xml-id: C1.S4.SS4.m1aadec
@@ Property / Symbols used @@
+base of natural logarithm
@@ Property / Symbols used: base of natural logarithm / rank @@
+Normal rank
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{e}}}$ 
\expe
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+xml-id: C4.S2.E11.m2aadec
@@ Property / Symbols used @@
+Q10771
@@ Property / Symbols used: Q10771 / rank @@
+Normal rank
@@ Property / Symbols used: Q10771 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\int}}$ 
\int
@@ Property / Symbols used: Q10771 / qualifier @@
+xml-id: C1.S4.SS4.m3aadec
@@ Property / Symbols used @@
+Q10816
@@ Property / Symbols used: Q10816 / rank @@
+Normal rank
@@ Property / Symbols used: Q10816 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$ 
\atan@@{\NVar{z}}
@@ Property / Symbols used: Q10816 / qualifier @@
+xml-id: C4.S23.SS2.p1.m7adec
@@ 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.m2adec
@@ Property / Symbols used @@
+Q10811
@@ Property / Symbols used: Q10811 / rank @@
+Normal rank
@@ Property / Symbols used: Q10811 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\Re}}$ 
\realpart@@
@@ Property / Symbols used: Q10811 / qualifier @@
+xml-id: C1.S9.E2.m1addec
@@ Property / Symbols used @@
+sine function
@@ Property / Symbols used: sine function / rank @@
+Normal rank
@@ Property / Symbols used: sine function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\sin\NVar{z}}}$ 
\sin@@{\NVar{z}}
@@ Property / Symbols used: sine function / qualifier @@
+xml-id: C4.S14.E1.m2adec
@@ Property / Symbols used @@
+Q12152
@@ Property / Symbols used: Q12152 / rank @@
+Normal rank
@@ Property / Symbols used: Q12152 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle x}}$ 
x
@@ Property / Symbols used: Q12152 / qualifier @@
+xml-id: C25.S1.XMD5.m1adec
@@ Property / Symbols used @@
+Q12161
@@ Property / Symbols used: Q12161 / rank @@
+Normal rank
@@ Property / Symbols used: Q12161 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle a}}$ 
a
@@ Property / Symbols used: Q12161 / qualifier @@
+xml-id: C25.S1.XMD6.m1ddec
@@ 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.m1edec
@@ 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.m1ddec

DLMF:25.14.E6 (Q7745): Difference between revisions

ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}

| z | = 1 , ℜ ⁡ a > 0 formulae-sequence 𝑧 1 𝑎 0 {\displaystyle{\displaystyle|z|=1,\Re a>0}}

Φ ⁡ ( z , s , a ) Lerch-Phi 𝑧 𝑠 𝑎 {\displaystyle{\displaystyle\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)}}

π {\displaystyle{\displaystyle\pi}}

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

e {\displaystyle{\displaystyle\mathrm{e}}}

∫ {\displaystyle{\displaystyle\int}}

arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

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

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

x 𝑥 {\displaystyle{\displaystyle x}}

a 𝑎 {\displaystyle{\displaystyle a}}

s 𝑠 {\displaystyle{\displaystyle s}}

z 𝑧 {\displaystyle{\displaystyle z}}

Latest revision as of 01:03, 2 January 2020

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${\displaystyle{\displaystyle\Re s>1}}$

${\displaystyle{\displaystyle|z|=1,\Re a>0}}$

${\displaystyle{\displaystyle\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)}}$

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

${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$

${\displaystyle{\displaystyle\mathrm{e}}}$

${\displaystyle{\displaystyle\int}}$

${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$

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

${\displaystyle{\displaystyle\Re}}$

${\displaystyle{\displaystyle\sin\NVar{z}}}$

${\displaystyle{\displaystyle x}}$

${\displaystyle{\displaystyle a}}$

${\displaystyle{\displaystyle s}}$

${\displaystyle{\displaystyle z}}$