1.7 Proof of Convergence

1.7 Proof of Convergence

  • In this section, we prove the theory of convergence.
  • There are three technical points that we state here, but most of the proof requires nothing more than simple math.

  • You are asked to verify Lemmas 1 and 2 in Exercises 1 and 2 of this section.
    • Section 6 proved Lemma 3.
  • This is where we are going to reference the theorem.

  • Now, using the equation.
  • The next step is to replace the sum with Lemma 2.

  • Substituting it in the book.

  • The second integral is seen in either case.

  • The last step is to show the integrals.
    • This is an exercise since the technique is the same as in Part 3.
  • The crux of the proof is to show the function from Eq.