Content-Length: 63714 | pFad | https://dlmf.nist.gov/./../././././././././././././bib/.././././front/.././5.3#F6

DLMF: §5.3 Graphics ‣ Properties ‣ Chapter 5 Gamma Function

About the Project

5 Gamma Function Properties 5.2 Definitions 5.4 Special Values and Extrema

§5.3 Graphics

ⓘ

Keywords:: gamma function, graphics
Permalink:: http://dlmf.nist.gov/5.3
See also:: Annotations for Ch.5

Contents

§5.3(i) Real Argument

ⓘ

Keywords:: convexity, gamma function, graphics, logarithm, psi function, reciprocal
Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/5.3.i
See also:: Annotations for §5.3 and Ch.5

See accompanying text — Figure 5.3.1: $\Gamma\left(x\right)$ and $1/\Gamma\left(x\right)$ . $x_{0}=1.46\dots$ , $\Gamma\left(x_{0}\right)=0.88\dots$ ; see §5.4(iii). Magnify

See accompanying text — Figure 5.3.2: $\ln\Gamma\left(x\right)$ . This function is convex on $(0,\infty)$ ; compare §5.5(iv). Magnify

See accompanying text — Figure 5.3.3: $\psi\left(x\right)$ . Magnify

§5.3(ii) Complex Argument

ⓘ

Keywords:: gamma function, graphics, psi function, reciprocal
Notes:: These surfaces were produced at NIST.
Permalink:: http://dlmf.nist.gov/5.3.ii
See also:: Annotations for §5.3 and Ch.5

In the graphics shown in this subsection, both the height and color correspond to the absolute value of the function. See also About Color Map.

See accompanying text — Figure 5.3.4: $|\Gamma\left(x+iy\right)|$ . Magnify 3D Help

See accompanying text — Figure 5.3.5: $1/|\Gamma\left(x+iy\right)|$ . Magnify 3D Help

See accompanying text — Figure 5.3.6: $|\psi\left(x+iy\right)|$ . Magnify 3D Help

5.2 Definitions 5.4 Special Values and Extrema

© 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