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

§25.3 Graphics

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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

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Symbols:: $\zeta\left(\NVar{s}\right)$ : Riemann zeta function and : real variable
Permalink:: http://dlmf.nist.gov/25.3.F1
Encodings:: pdf, png
See also:: Annotations for §25.3 and Ch.25

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

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Symbols:: $\zeta\left(\NVar{s}\right)$ : Riemann zeta function and : real variable
Permalink:: http://dlmf.nist.gov/25.3.F2
Encodings:: pdf, png
See also:: Annotations for §25.3 and Ch.25

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

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Symbols:: $\zeta\left(\NVar{s}\right)$ : Riemann zeta function, $\mathrm{i}$ : imaginary unit and : real variable
Permalink:: http://dlmf.nist.gov/25.3.F3
Encodings:: Vizualization, pdf, png
See also:: Annotations for §25.3 and Ch.25

See accompanying text

Figure 25.3.4:

, $0\leq t\leq 50$ .

and $\zeta\left(\tfrac{1}{2}+it\right)$ have the same zeros. See §25.10(i). Magnify

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Symbols:: $\zeta\left(\NVar{s}\right)$ : Riemann zeta function, $\mathrm{i}$ : imaginary unit and : zeros function
Permalink:: http://dlmf.nist.gov/25.3.F4
Encodings:: pdf, png
See also:: Annotations for §25.3 and Ch.25

See accompanying text

Figure 25.3.5:

, $1000\leq t\leq 1050$ . Magnify

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Symbols:: : zeros function
Permalink:: http://dlmf.nist.gov/25.3.F5
Encodings:: pdf, png
See also:: Annotations for §25.3 and Ch.25

See accompanying text

Figure 25.3.6:

, $10000\leq t\leq 10050$ . Magnify

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Symbols:: : zeros function
Permalink:: http://dlmf.nist.gov/25.3.F6
Encodings:: pdf, png
See also:: Annotations for §25.3 and Ch.25

25.2 Definition and Expansions 25.4 Reflection Formulas

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