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

From DRMF

Jump to navigation Jump to search

← Older edit

Revision as of 13:49, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:49, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(4 intermediate revisions by the same user not shown)
		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

---

Latest revision as of 13:49, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:25.12.E12	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathrm{Li}_{s}\left(z\right)=\Gamma\left(1-s\right)\left(\ln\frac{1}{z}\right)^{s-1}+\sum_{n=0}^{\infty}\zeta\left(s-n\right)\frac{(\ln z)^{n}}{n!},}}$

0 references

DLMF id

DLMF:25.12.E12

0 references

constraint

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

0 references

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

0 references

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

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aadec

0 references

Riemann zeta function

Defining formula

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

xml-id

C25.S2.E1.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2addec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5adec

0 references

principal branch of logarithm function

Defining formula

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

xml-id

C4.S2.E2.m2aedec

0 references

polylogarithm

Defining formula

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

xml-id

C25.S12.E10.m2abdec

0 references

Q12148

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C25.S1.XMD3.m1edec

0 references

Q12149

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C25.S1.XMD7.m1bdec

0 references

Q12156

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C25.S1.XMD8.m1gdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7731&oldid=40540"