Solution

In[1]:=

Out[1]=

In[2]:=

Out[2]=

In[3]:=

Out[3]=

The function Random[] requires no argument (allthough you can give it some). For each point to be plotted, Mathematica computes a random number. When increasing the value of option PlotPoints, the graph of Random[] approaches a black box. The default value of PlotPoints is 15.

In[6]:=

Out[6]=

In[7]:=

Out[7]=

In the following, I will plot four Bessel functions in the same figure and distinguish them by color, using the option PlotStyle. The graphics directives, such as RGBColor, will be applied cyclically to the list of functions to be plotted.

In[8]:=

Out[8]=

In[9]:=

Out[9]=

For non-integer arguments of the factorial function, Mathematica automatically uses the generalized factorial function, i.e. the gamma function instead. See the help file for Factorial and Gamma for more information.

Created by Mathematica  (April 10, 2007)