Integrating e^x^2: Proof & Explanation

Click For Summary
SUMMARY

The integral of e^x^2 cannot be expressed as an elementary function, as established by Liouville's theorem. This theorem provides a framework for understanding the limitations of integration in terms of elementary functions. The discussion references "Algorithms for Computer Science" by Geddes as a valuable resource for further exploration of this topic. The consensus among participants is that traditional integration methods fail to yield a solution for e^x^2.

PREREQUISITES
  • Understanding of Liouville's theorem
  • Familiarity with elementary functions
  • Basic knowledge of integration techniques
  • Awareness of algorithmic concepts in computer science
NEXT STEPS
  • Study Liouville's theorem in detail
  • Read "Algorithms for Computer Science" by Geddes
  • Explore advanced integration techniques beyond elementary functions
  • Investigate the properties of special functions related to e^x^2
USEFUL FOR

Mathematicians, computer scientists, and students studying advanced calculus or integration techniques will benefit from this discussion.

l-1j-cho
Messages
104
Reaction score
0
I went through several threads about the integral of e^x^2
but I could not find anything about the proof why e^x^2 cannot be integrated as an elementry function.
Could you explain why?
 
Physics news on Phys.org
Check Liouville's theorem. A good reference is "Algorithms for computer science" by Geddes, which explains these things in detail!
 
l-1j-cho said:
I went through several threads about the integral of e^x^2
but I could not find anything about the proof why e^x^2 cannot be integrated as an elementry function.
Could you explain why?

I dunno. Maybe because all of the ordinary methods don't work.. maybe this will help.

http://en.wikipedia.org/wiki/Elementary_function
 

Similar threads

  • · Replies 27 ·
Replies
27
Views
3K
  • · Replies 14 ·
Replies
14
Views
4K
  • · Replies 29 ·
Replies
29
Views
5K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 3 ·
Replies
3
Views
4K