# riemann

1. ### Could someone please explain how a specific part of the expression for the Riemann su

I'm really sorry if this post is not appropriate for this forum. My math level is quite low and it might have been because of that I could not understand this concept. So, the problem that I have is that I don't understand how a part of this expression is generated: 1. S =\sum_{i=1}^n 2...
2. ### Note on the Riemann hypothesis

It is well known that there is some freedom, at times, to do order of operations in algebra is different orders. We might choose to do a distributive operation before an additive one, for instance. Suppose we we use that freedom not to do the additive absorptive operation of infinity until it...
3. ### Proof of Riemann Hypothesis

Sir Michael Atiyah is a huge name in mathematics. He's one of the best mathematicians alive today. He has proven the famous Atiyah-Singer index theorem, and has won a Fields medal. What's more, at 90(!!) years of age, he will present this monday a proof of the Riemann hypothesis, arguably the...
4. ### Self-studying multiple Riemann integrals

As the title says, I would like to self-study multivariable real analysis (integration, specifically; the Riemann integral) and I need some recommendations (resources, books, videos, ...). I'm from Croatia and got my hands on some Croatian notes about multivariable real analysis so if some of...
5. ### Riemann sums problem

Hello! I am struggling with approaching the following problem: \lim_{n\to\infty} \sum_{k=1}^{n} \frac{n}{\sqrt{n^4 + k^2}} I know that I probably have to use something like the following: \lim_{n\to\infty}\frac{b-a}{n} \sum_{k=1}^{n}f(x_k) = \int_a^b f(x) dx ... but currently I'm in a block...
6. ### Lebesgue integration - Riemann integration

What the differences between Lebesgue integration and Riemann integration?
7. ### Riemann's Sum Problem

Brief Overview What I've done so far: The Question If the safety capacity for the benign use of a camping gas lamp inside a confined space is (104Ã·5) m^3, calculate whether it would be safe to use the lamp within the lightweight â€˜pop-upâ€™ tent. I know the height of my tent is...
8. ### Riemann Sphere

What is the connection between Riemann Sphere to Trigonometric Functions?
9. ### Riemann hypothesis

how to solve Riemann hypothesis
10. ### My elegant formula for the Harmonic Numbers of order k

I'm looking for someone who can "introduce" me to the arXiv.org site, so I can upload a paper that demonstrates my elegant formula for the Harmonic Numbers of order k. Because I no longer have a university email, and haven't published in my undergrad years, there's this little obstacle that you...
11. ### Riemann Hypothesis

P: Î¶(sáµ¢)=0 Q: sáµ¢=Ïƒ+it R: tâ‰ 0 S: Ïƒ=1/2 A: Pâ‰¡[Qâ‰¡(Râ‰¡S)] It is that Î¶(1/2)=0 if the Proposition A doesn't hold, but actually, Î¶(1/2)â‰ˆ-1.4603545; therefore RH does hold.
12. ### Use the definition of the integral as a limit of a Riemann sum

Equation: "integral from 0 to 6 of -(x^2)+36" I know how to find it the easy way... Ex.) I know to take the integral -(x^3)/3+36x and evaluate it from 0 to 6 which = (-216/3) + 216 == [144] So I know the answer, I just don't understand what my teacher wants. I know there's an...
13. ### Riemann hypothesis

Hello, I am looking for a good read or video about the Riemann zeta function and its distribution of prime numbers, if anyone knows of any.
14. ### Solving Riemann Lower sum

I'm trying to find the integral of f(x)=x^{2},f:[0,1]\rightarrow \mathbb{R} using Riemann's criterion. I created a partition with equal intervals like this P_{n}=\{0<\frac{1}{n}<\frac{2}{n}<...<\frac{n-1}{n}=1\} and then I started cxalculating the lower sum...
15. ### Riemann Sums

$\lim_{n \to \infty} \sum_{i=0}^n sin \left[ \left( 2 + \frac{3}{2n} \right) + \frac{3}{n}i \right] \cdot \frac{3}{n} ~=~ \int_a^b \sin(x)$ dx What will be the value of b and a?
16. ### Riemann Sums and Definite Integrals

Use Example 1 as a model to evaluate the limit \lim _{n\to \infty }\left(\sum _{i=1}^n\left(f\left(ci\right)Î”xi\right)\right) over the region bounded by the graphs of the equations. (Round your answer to three decimal places.) f(x) = sqrt(x), y = 0, x = 0, x = 3 HINT: Let...
17. ### Find the Riemann Sum

Find the Riemann sum for f(x) = x2 + 3x over the interval [0, 8], where x0 = 0, x1 = 1, x2 = 2, x3 = 7, and x4 = 8, and where c1 = 1, c2 = 2, c3 = 5, and c4 = 8. I'm confused. What do the c's and x's mean again? I know, I'm dumb and have no clue on where to begin.