Note: if you can't figure out the tune to this song and the proper pronunciation of the word "funct" after the first verse, you had a very fortunate childhood. As with the log song, all the mathematics are correct. (a_n means a with subscript n; it should just be read "a n".) If someone out there knows of a way to get subscripts and superscripts, I'd love to hear how: email me at jeffs@math.bu.edu
Here's the story
Of a power series
a_n over n factorial x to the n
Where the a_n's are just deriv'tives
With a zero plugged in.
Here's the story
Of the remainder
Which is just like the next term that you should get
But instead of inputting zero
Plug in c instead.
One day this R_n met this series
And they knew that it was much more than a hunch
That if R_n should tend to zero
The series would approach the funct.
The Taylor funct.
The Taylor funct.
That's the way we derive the Taylor funct!