Content-Length: 52585 | pFad | https://dlmf.nist.gov/./././././././././../././././bib/.././././././././././././.././././25.3.F4

6000 DLMF: §25.3 Graphics ‣ Riemann Zeta Function ‣ Chapter 25 Zeta and Related Functions

About the Project

25 Zeta and Related Functions Riemann Zeta Function 25.2 Definition and Expansions 25.4 Reflection Formulas

§25.3 Graphics

ⓘ

Keywords:: Riemann zeta function, graphics
Notes:: These graphics were constructed at NIST.
Permalink:: http://dlmf.nist.gov/25.3
See also:: Annotations for Ch.25

See accompanying text — Figure 25.3.1: Riemann zeta function $\zeta\left(x\right)$ and its derivative $\zeta'\left(x\right)$ , $-20\leq x\leq 10$ . Magnify

See accompanying text — Figure 25.3.2: Riemann zeta function $\zeta\left(x\right)$ and its derivative $\zeta'\left(x\right)$ , $-12\leq x\leq-2$ . Magnify

See accompanying text — Figure 25.3.3: Modulus of the Riemann zeta function $|\zeta\left(x+iy\right)|$ , $-4\leq x\leq 4$ , $-10\leq y\leq 40$ . Magnify 3D Help

See accompanying text — Figure 25.3.4: $Z(t)$ , $0\leq t\leq 50$ . $Z(t)$ and $\zeta\left(\tfrac{1}{2}+it\right)$ have the same zeros. See §25.10(i). Magnify

See accompanying text — Figure 25.3.5: $Z(t)$ , $1000\leq t\leq 1050$ . Magnify

See accompanying text — Figure 25.3.6: $Z(t)$ , $10000\leq t\leq 10050$ . Magnify

25.2 Definition and Expansions 25.4 Reflection Formulas

© 2010–2024 NIST / Disclaimer / Feedback; Version 1.2.3; Release date 2024-12-15.

NIST

Site Privacy Accessibility Privacy Program Copyrights Vulnerability Disclosure No Fear Act Policy FOIA Environmental Policy Scientific Integrity Information Quality Standards Commerce.gov Science.gov USA.gov