You get a bonus - 1 coin for daily activity. Now you have 1 coin

Polylogarithm

Lecture



Polylogarithm is a special function denoted by Polylogarithm and defined as an infinite power series

Polylogarithm

where s and z are complex numbers, and Polylogarithm . For other z, a generalization is made using analytic continuation.

Polylogram heights on the complex plane

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

A special case is Polylogarithm in which Polylogarithm . Functions Polylogarithm and Polylogarithm were named dilogarithm and trilogarithm respectively. For polylogarithms of various orders, the ratio

Polylogarithm

Alternative definitions of the polylogarithm are Fermi-Dirac and Bose-Einstein integrals.

Partial Values

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Polylogarithm

Literature

  • Abel NH compuvres complètes de Niels Henrik Abel - Nouvelle édition, Tome II. - Christiania [Oslo]: Grøndahl & Søn, 1881. - P. 189–193. (this 1826 manuscript was only published posthumously.)
  • Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. - New York: Dover Publications, 1972. - ISBN 0-486-61272-4.
  • (April 1997) "On the Rapid Computation of Various Polylogarithmic Constants" (PDF). Mathematics of Computation 66 (218): 903–913. DOI: 10.1090 / S0025-5718-97-00856-9.

See also

created: 2014-10-25
updated: 2024-11-14
368



Rating 9 of 10. count vote: 2
Are you satisfied?:



Comments


To leave a comment
If you have any suggestion, idea, thanks or comment, feel free to write. We really value feedback and are glad to hear your opinion.
To reply

Comprehensive analysis and operational calculus

Terms: Comprehensive analysis and operational calculus