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FunctionAdvisor/plot

2D and 3D plots illustrating a mathematical function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

FunctionAdvisor(plot, math_function)

Parameters

plot

-

literal name;'plot'

math_function

-

name of a known mathematical function; see FunctionAdvisor(known_functions)

Description

• 

The FunctionAdvisor(plot math_function) command displays 2D and 3D plots illustrating math_function following, where possible, the NIST Digital Library of Mathematical Functions.

• 

The 3D plots displayed by FunctionAdvisor(plot math_function) involve three kinds of plot structures. First there are the standard 3D plots you can construct using plot3d, used for instance for some functions of many arguments provided that the function is real for real values of its arguments. Second, there are 3D plots constructed using plots:-complexplot3d, where the vertical axis represent the absolute value of the function and the two horizontal axes represent the Real and Imaginary parts of the main plotting complex variable. Finally, some plots are obtained using plots:-plotcompare with the option expression_plot, appropriate to illustrate branch cuts.

• 

After displaying the plots on the screen, the actual value returned by FunctionAdvisor(plot math_function) is NULL. You can get the plots structures themselves in two different ways: right-click the plot, copy, then paste into an input region, or use MathematicalFunctions:-Get(plot, math_function) as shown in the last example.

Examples

2D and 3D plots illustrating the natural logarithm, respectively of a real and complex variable

FunctionAdvisorplot,ln

You can rotate the 3D plots with the mouse. Also, by right-clicking any of the 2D or 3D plots you can change the way the plot is presented in different ways (Style, Color, Orientation, etc.)

Note the similarity between the 2D plots of ln and the exponential integral Ei function of a real variable; over the complex plane, however, these functions behave rather different

FunctionAdvisorplot,Ei

In most cases, when a function involves different number of arguments, plots for the different cases are presented, for example GAMMA represents both the Gamma function (case of 1 argument) and the incomplete gamma function (case of 2arguments)

FunctionAdvisorplot,Γ

The 2D plots of the JacobiSN (elliptic sin function) of a real variable resemble the plots for sin

FunctionAdvisorplot,JacobiSN

2D and 3D plots illustrating the important 2F1 case of the generalized hypergeometric function

FunctionAdvisorplot,hypergeom

To get the plot structure itself, for instance those for the hypergeometric function displayed above, use

plots_hypergeomMathematicalFunctions:-Getplot,hypergeom

plots_hypergeom,

Having the plotting structures assigned to plots_hypergeom you can now manipulate each plot as desired, for example, consider the 2nd 2D plot:

plots_hypergeom12

Change the title, the color, and make the plot be constrained (note the use of the keyword overrideoptions of plots:-display)

plots:-displayplots_hypergeom12,overrideoptions,color=Blue,axes=boxed,scaling=constrained,title=2F1 hypergeometric function

See Also

abs

Ei

FunctionAdvisor

GAMMA

hypergeom

Im

JacobiSN

ln

MathematicalFunctions:-Get

plot3d

plots:-compare

plots:-complexplot3d

plots:-display

Re