What is the meaning of the subscript in the polygamma function?

  • Thread starter rman144
  • Start date
  • Tags
    Function
In summary, the conversation discusses a partial sum formula for a summation involving the polygamma function and the subscript e^(2/x), which is not fully understood. The speaker expresses confusion about the terminology involving psi and asks for clarification.
  • #1
rman144
35
0
So I've been working on a proof and Wolfram Alpha gives the following partial sum formula for one of the summations in the proof:

http://www.wolframalpha.com/input/?i=sum[e^(-(2k+1)/x)/(1+e^(-(2k+1)/x)+)^2+]

What does the terminology involving psi mean? I think it is the first derivative of the polygamma function, but I don't understand what the subscript e^(2/x) means.

Thanks in advance for the help.
 
Physics news on Phys.org
  • #2
I don't know what that subscript means either. It's funny that W|A thinks that it needs to tell you what the natural logarithm is but not the (variant of the) trigamma function.
 

FAQ: What is the meaning of the subscript in the polygamma function?

1. What is the polygamma function?

The polygamma function, also known as the digamma function, is a special mathematical function that is the derivative of the logarithm of the gamma function. It is denoted by the Greek letter "ψ" followed by a subscript indicating the number of times it is differentiated.

2. What is the purpose of the polygamma function?

The polygamma function is used in various mathematical and scientific fields, such as statistics, number theory, and physics. It is particularly useful in evaluating complex integrals and solving differential equations.

3. How is the polygamma function calculated?

The polygamma function can be calculated using various methods, such as series expansions, continued fractions, and recurrence relations. It can also be approximated using numerical methods, such as Taylor series expansions or computer algorithms.

4. What are the applications of the polygamma function?

The polygamma function has various applications in mathematics, such as calculating sums and integrals, finding solutions to differential equations, and evaluating complex functions. It also has applications in physics, such as in quantum mechanics and statistical mechanics.

5. Are there any special properties of the polygamma function?

Yes, the polygamma function has several special properties, such as the reflection formula, the duplication formula, and the recurrence relation. It also has connections to other special functions, such as the Riemann zeta function and the beta function.

Similar threads

Replies
1
Views
2K
Replies
15
Views
2K
Replies
9
Views
2K
Replies
2
Views
2K
Replies
6
Views
2K
Back
Top