Why Does This Polylogarithm Identity Have No Restrictions?

  • Context: Graduate 
  • Thread starter Thread starter rman144
  • Start date Start date
  • Tags Tags
    Identity
Click For Summary
SUMMARY

The discussion centers on a polylogarithm identity found on Wolfram, specifically at the URL provided. The identity raises questions regarding the absence of restrictions despite the gamma function's poles at negative integers. Participants clarify that the lack of restrictions is due to the identity's structure, where one side is undefined at the same points as the other, thus avoiding contradictions in the equation.

PREREQUISITES
  • Understanding of polylogarithm functions
  • Familiarity with the gamma function and its properties
  • Knowledge of the Riemann zeta function and its behavior
  • Basic concepts of complex analysis, particularly regarding poles
NEXT STEPS
  • Research the properties of the gamma function, focusing on its poles and residues
  • Explore the implications of the Riemann zeta function in relation to polylogarithms
  • Study complex analysis techniques for handling undefined points in functions
  • Examine additional polylogarithm identities and their restrictions or lack thereof
USEFUL FOR

Mathematicians, students of complex analysis, and anyone interested in advanced functions and their properties, particularly in relation to polylogarithms and special functions.

rman144
Messages
34
Reaction score
0
I found this equation last night on Wolfram:

http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/PolyLog/06/03/0001/

How is it possible this equation has no restrictions given that the gamma function has poles at the negative integers?

Also, won't the zeta function portion run into problems at those integers as well when k passes v in the summation?
 
Physics news on Phys.org
There are no restrictions because one side is not defined at exactly the points the other is not defined.
 

Similar threads

MHB The Barnes' G-Function, and related higher functions
  • · Replies 35 ·
2
Replies
35
Views
27K
Requesting suggestions for languages, libraries, and architectures for parallel (and sometimes non parallel) numerical and scientific computations
  • · Replies 8 ·
Replies
8
Views
5K
Challenge Math Challenge - November 2018
  • · Replies 175 ·
6
Replies
175
Views
28K
Mathematica This Week's Finds in Mathematical Physics (Week 217)
  • · Replies 2 ·
Replies
2
Views
3K
April Fool's Physics Papers 2026
  • · Replies 3 ·
Replies
3
Views
816
What is the CORDIC Algorithm and How Does it Work?
  • · Replies 1 ·
Replies
1
Views
4K
Graduate How Does the Double-Slit Experiment Illustrate Wave-Particle Duality?
  • · Replies 1 ·
Replies
1
Views
3K
Schools How well does this course prepare me for college math?
  • · Replies 10 ·
Replies
10
Views
5K
Mathematica This Week's Finds in Mathematical Physics (Week 259)
  • · Replies 1 ·
Replies
1
Views
4K
Mathematica This Week's Finds in Mathematical Physics (Week 244)
  • · Replies 1 ·
Replies
1
Views
3K