#zeta function

[still-searching-for-et]

Who says you can’t do complex analysis in Excel...

Prime Counting function using the first 200 non trivial zeroes of the Zeta function (and first 5 trivial ones).  Equation used is the main sum in the top with an approximation if you want a simpler expression to try.

Main point of the famous paper by Riemann is using the zeta zeroes you can calculate the number of primes below a number, they are one in the same, interwoven in math.

The zeroes can be found easiest using the Riemann Siegel functions lower graph (also just using excel).

[numb3rth30ry]

We’re doomed.

[teratosapphic]

hey mathy side of tumblr

since  ζ(-1) is the infinite sum of all natural natural numbers, and also equals -1/12, would 2 * ζ(-1) = -1/6, -1/12, or -1/24?

[adhdphysicist]

check out this awesome riemann zeta function poster i got from 3blue1brown’s store!! his video on the zeta function was actually the video that got me into his channel, i totally recommend it!

[bookpiofficial]

A zeta function Computation of Casimir Energy | Chapter 05 | Advances in Mathematics and Computer Science Vol. 4

A computation of Casimir energy via spectral zeta function is considered in this Chapter. The original computations deriving the Casimir energy and force consists of first taking limits of the spectral zeta function and afterwards analytically extending the result. This process of computation presents a weakness in Hendrik Casimir’s original argument since limit and analytic continuation do not commute. A case of the Laplacian on a parallelepiped box representing the space as the vacuum between two plates modelled with Dirichlet and periodic Neumann boundary conditions is constructed to address this anomaly. It involves the derivation of the regularised zeta function in terms of the Riemann zeta function on the parallelepiped. The values of the Casimir energy and Casimir force obtained from our derivation agree with those of Hendrik Casimir.

Author(s) Details

Dr. Louis Omenyi Department of Mathematics/Computer Science/Statistics/Informatics, Alex Ekwueme Federal University, Ndufu-Alike, Nigeria.

View Volume: http://bp.bookpi.org/index.php/bpi/catalog/book/97

[numb3rth30ry]

Sorcery.

[tunnels-end]

π²/6

[scirp]

Read the full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=49482 DOI: 10.4236/am.2014.516246 Author(s) Haifeng Xu, Jiuru Zhou Affiliation(s) School of Mathematical Sciences, Yangzhou University, Jiangsu, China. School of Mathematical Sciences, Yangzhou University, Jiangsu, China. ABSTRACT By using Fubini theorem or Tonelli theorem, we find that the zeta function value at 2 is equal to a special integral. Furthermore, we find that this special integral is two times of another special integral. By using this fact we give an easy way to calculate the value of the alternating sum of without using the Fourier expansion. Also, we discuss the relationship between Genocchi numbers and Bernoulli numbers and get some results about Bernoulli polynomials.eww140917gjr KEYWORDS Basel Problem, Zeta Function, Bernoulli Numbers, Bernoulli Polynomials