Chebyshev Polynomials

The applet below depicts Chebyshev polynomials of the first kind Tn(x) = cos(n·arccos(x)), n = 0, ..., 50.

As of 2018, Java plugins are not supported by any browsers (find out more). This Wolfram Demonstration, Chebyshev Polynomials, shows an item of the same or similar topic, but is different from the original Java applet, named 'ChebyshevTest'. The originally given instructions may no longer correspond precisely.

(image below from deprecated 'ChebyshevTest' applet)

Chebyshev Polynomials, plenty

The applet displays the sequence of polynomials PMin through PMax, inclusive. When sufficiently many (30 above) of the polynomial graphs are displayed simultanesoiusly, one can see "ghost lines" -- empty spaces left untouched by the graphs. What are they?

Both Min and Max numbers in the applet can be clicked on off their vertical center line. To increase the number click to the right of its center line, to decrease it click to the left. Dragging the cursor will speed up the process. 50 is the maximum value for both.

When plenty of the polynomials are graphed there appear some ghost images. What are these?


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