Ivan Shishkin, Rye (1878)

Problems/Real analysisUnreviewed

Une intégrale complètement nulle !

by mathman·
50
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
·
Français
FrançaisAdd translation

Showing the Français version because no English translation exists yet. Add that translation.

Unreviewed. This problem has not been reviewed by trusted users yet.

Pour x∈Rx\in \mathbb{R}, x≥1x\geq 1 et pp parcourt les nombres premiers, on définit les deux fonctions:

θ(x)=∑p≤xln(p)\theta(x)=\sum_{p\leq x}ln(p) (première fonction de Tchebychev)
π(x)=∑p≤x1\pi(x)=\sum_{p\leq x}1

Montrez que : ∫1+∞θ(t)+π(t)−π(t)ln(t)t2dt=0\int_{1}^{+\infty} \frac{\theta(t)+\pi (t)-\pi(t)ln(t)}{t²}dt=0

I solved itMark it doneAdd to my listKeep it in your list
I like this problem0 likes
Show related problems0

No related problems yet.

Hints

3

Hint 1

Open this only if you want a small nudge before looking at the solutions.

Solutions

0
Report

For an unclear, ambiguous, or possibly incorrect statement, please use the Discussion tab on the right. Report content that needs moderator intervention, such as dangerous, clearly non-mathematical, or plagiarized content.