Copyright 2005 by Jeff Suzuki
I can't recall the circumstances of this song, other than the fact that it was written after the log song and I had to prove to myself that I could write more than one song. "Funct" should be pronounced as the first syllable in function, and sub/superscripts should just be read: an is "ay-en"; the tune is the Brady Bunch theme song.
If you want to be picky, then technically the song is about the Maclaurin series. But Taylor scans better, and as it includes the Maclaurin series as a subset, and I claim aesthetic choice...
Here's the story. Of a power series. Sum of an xn o'er factorial n,
Where the an's
Are just deriv'tives.
With a zero plugged in.
Here's the story.
Of the remainder.
Which is just like the nice term that you should get.
But instead of
Inputting zero,
Plug in c instead.
One day this remainder met this series
And they both knew that it was much more than a hunch.
That if Rn should tend to zero,
The series would approach the funct.
The Taylor funct!
The Taylor funct!
That's the way we obtain
The Taylor funct!