When can interchange sum and integral

  • Context: Graduate 
  • Thread starter Thread starter Aziza
  • Start date Start date
  • Tags Tags
    Integral Sum
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
2 replies · 4K views
Aziza
Messages
189
Reaction score
1
Why in the attached picture is it legal to interchange the sum and integral? Is it just because n is not dependent on t? note: (c1)n is just a function of n
 

Attachments

  • intgeral-sum.jpeg
    intgeral-sum.jpeg
    50.2 KB · Views: 779
Physics news on Phys.org

Discussion

You would have to apply something like the monotone or dominated convergence theorem to prove that it is valid in this case.
 
The reason you can interchange is not because the variables are independent but because the operations are; that is, the integration and the summation.
 
Last edited:

Similar threads

Graduate Why Is It Acceptable to Interchange Sum and Integral for Martingale Proof?

  • osprey
  • · Replies 1 ·
  • Set Theory, Logic, Probability, Statistics
Replies
1

Graduate Can You Interchange Derivatives and Integrals in Different Variables?

  • Hertz
  • · Replies 1 ·
  • Calculus
Replies
1

Graduate Can you interchange limit and integral for e^(-γ|x|)f(x)?

  • keniwas
  • · Replies 1 ·
  • Calculus
Replies
1

Graduate When Can Differentiation Be Interchanged with Integration?

  • Galileo
  • · Replies 23 ·
  • Calculus
Replies
23