Digital Library of Mathematical Functions

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5 Gamma Function Properties 5.2 Definitions 5.4 Special Values and Extrema

§5.3 Graphics

Keywords:: gamma function
Permalink:: http://dlmf.nist.gov/5.3

Contents

§5.3(i) Real Argument
§5.3(ii) Complex Argument

§5.3(i) Real Argument

Notes:: These graphs were produced at NIST.
Keywords:: gamma function, psi function
Permalink:: http://dlmf.nist.gov/5.3.i

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Figure 5.3.1: $\mathop{\Gamma\/}\nolimits\!\left(x\right)$ and $1/\mathop{\Gamma\/}\nolimits\!\left(x\right)$ . $x_{0}=1.46\dots$ , $\mathop{\Gamma\/}\nolimits\!\left(x_{0}\right)=0.88\dots$ ; see §5.4(iii).

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Symbols:: $\mathop{\Gamma\/}\nolimits\!\left(z\right)$ : gamma function and : real variable
Referenced by:: §5.4(iii)
Permalink:: http://dlmf.nist.gov/5.3.F1
Encodings:: pdf, png

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Figure 5.3.2: $\mathop{\ln\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(x\right)$ . This function is convex on $(0,\infty)$ ; compare §5.5(iv).

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Symbols:: $\mathop{\Gamma\/}\nolimits\!\left(z\right)$ : gamma function, $\mathop{\ln\/}\nolimits z$ : principal branch of logarithm function, : open interval and : real variable
Permalink:: http://dlmf.nist.gov/5.3.F2
Encodings:: pdf, png

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Figure 5.3.3: $\mathop{\psi\/}\nolimits\!\left(x\right)$ .

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Symbols:: $\mathop{\psi\/}\nolimits\!\left(z\right)$ : psi (or digamma) function and : real variable
Permalink:: http://dlmf.nist.gov/5.3.F3
Encodings:: pdf, png

§5.3(ii) Complex Argument

Notes:: These surfaces were produced at NIST.
Keywords:: gamma function, psi function
Permalink:: http://dlmf.nist.gov/5.3.ii

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

Visualization Help

Figure 5.3.4: $|\mathop{\Gamma\/}\nolimits\!\left(x+iy\right)|$ .

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Symbols:: $\mathop{\Gamma\/}\nolimits\!\left(z\right)$ : gamma function, : real variable and : real variable
Referenced by:: Graphics
Permalink:: http://dlmf.nist.gov/5.3.F4
Encodings:: VRML, X3D, pdf, png

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Visualization Help

Figure 5.3.5: $1/|\mathop{\Gamma\/}\nolimits\!\left(x+iy\right)|$ .

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Symbols:: $\mathop{\Gamma\/}\nolimits\!\left(z\right)$ : gamma function, : real variable and : real variable
Permalink:: http://dlmf.nist.gov/5.3.F5
Encodings:: VRML, X3D, pdf, png

See accompanying text

Visualization Help

Figure 5.3.6: $|\mathop{\psi\/}\nolimits\!\left(x+iy\right)|$ .

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Symbols:: $\mathop{\psi\/}\nolimits\!\left(z\right)$ : psi (or digamma) function, : real variable and : real variable
Referenced by:: Graphics
Permalink:: http://dlmf.nist.gov/5.3.F6
Encodings:: VRML, X3D, pdf, png

© 2010–2013 NIST / Privacy Policy / Disclaimer / Feedback; Version 1.0.6; Release date 2013-05-06 Math-Image version (See MathML) . A Printed Companionis available. 5.2 Definitions 5.4 Special Values and Extrema

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