Why Does This Polylogarithm Identity Have No Restrictions?

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In summary, a polylogarithm identity is a mathematical equation that relates different polylogarithmic functions and allows for the simplification and manipulation of complex expressions. Some common identities include the Euler identity, the Clausen identity, and the Landen transformation, and they are used in various branches of mathematics such as number theory, complex analysis, and algebraic geometry. The significance of polylogarithm identities lies in their role in the study of special functions and their applications in fields such as physics, engineering, and computer science. However, there are still many open problems and unsolved questions related to polylogarithm identities, such as finding new identities and exploring their connections with other areas of mathematics.
  • #1
rman144
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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?
 
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  • #2
There are no restrictions because one side is not defined at exactly the points the other is not defined.
 

FAQ: Why Does This Polylogarithm Identity Have No Restrictions?

What is a polylogarithm identity?

A polylogarithm identity is a mathematical equation that relates different polylogarithmic functions. These functions are defined as the sum of powers of a variable raised to different exponents, and the identities provide a way to simplify and manipulate these expressions.

What are some common polylogarithm identities?

Some common polylogarithm identities include the Euler identity, the Clausen identity, and the Landen transformation. These identities can be used to express complex polylogarithmic functions in terms of simpler ones.

How are polylogarithm identities used in mathematics?

Polylogarithm identities are used in various branches of mathematics, including number theory, complex analysis, and algebraic geometry. They allow for the simplification and manipulation of complex expressions, and can also provide insights into the behavior of certain functions.

What is the significance of polylogarithm identities?

Polylogarithm identities play an important role in many areas of mathematics, particularly in the study of special functions. They also have applications in physics, engineering, and computer science, where they are used in the analysis of complex systems and algorithms.

Are there any open problems or unsolved questions related to polylogarithm identities?

Yes, there are still many open problems and unsolved questions related to polylogarithm identities. Some of these include finding new identities, proving theorems about their properties, and exploring their connections with other areas of mathematics.

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