What Is the Arithmetic Gamma Function \(\gamma_{m}(n)\)?

Click For Summary

Discussion Overview

The discussion revolves around the definition and understanding of the arithmetic gamma function \(\gamma_{m}(n)\), which appears in certain exercises. Participants are seeking clarification on its meaning and context, as well as its relation to other known gamma functions.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant expresses confusion about the definition of \(\gamma_{m}(n)\) and notes difficulty in finding information online, particularly due to confusion with the standard gamma function.
  • Another participant mentions the incomplete gamma function, suggesting a potential connection but noting that it appears different from the function in question.
  • Two participants request that the original poster share specific exercises to provide context, indicating that understanding the exercises may help identify the function.

Areas of Agreement / Disagreement

Participants do not appear to have a consensus on the definition of \(\gamma_{m}(n)\), and multiple viewpoints regarding its potential relation to other gamma functions exist. The discussion remains unresolved.

Contextual Notes

The discussion lacks specific definitions or examples of the arithmetic gamma function, and the relationship to the incomplete gamma function is not fully explored. There are also no clear assumptions or contexts provided for the exercises mentioned.

elibj123
Messages
237
Reaction score
2
In some exercises I've stumbled upon a function which is denoted \gamma_{m}(n) with m,n natural. I've no idea what is the definition of the function and could not infer from the exercises. Searching google yielded nothing, as it kept suggesting me the OTHER Gamma function.
Can anyone here help me please?

Thanks in advance
 
Physics news on Phys.org
There is something called the incomplete gamma function which uses the symbol (lower case gamma) that you have, but it does look a little different.
 
elibj123,

Post some of the exercises. Perhaps someone will recognize it from the context.
 
Stephen Tashi said:
elibj123,

Post some of the exercises. Perhaps someone will recognize it from the context.
And what he is actually studying! (if not clear from the exercise)
 

Similar threads

Graduate What is the unique special function in this integral problem?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad On integral of simple function and representation
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Puzzled about Section 3.12 of Jackson's E&M book
  • · Replies 18 ·
Replies
18
Views
3K
Graduate Recover Hamilton equation from 2-form defined on phase space
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Resonant frequencies of liquid in a cylinder
  • · Replies 14 ·
Replies
14
Views
3K
Application of Residue Theorem to Definite Integrals (Logarithm)
  • · Replies 9 ·
Replies
9
Views
6K
Solving Modulo Arithmetic Problem with Variable Integer k
  • · Replies 5 ·
Replies
5
Views
2K
What Are the Values of f(3), f(4), and f(5) in the Gamma Function?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Derivatives and Integrals of the Hurwitz Zeta function
  • · Replies 2 ·
Replies
2
Views
15K
Derivative of Cost Function with Respect to Output Layer Weight
  • · Replies 31 ·
2
Replies
31
Views
4K