Section 25.6 Connecting to Zeros
Subsection 25.6.1 Where are the zeros?
Our next goal is to see how this connectionxxxxxxxxxx
L = lcalc.zeros_in_interval(10,100,0.1)
[l[0] for l in L]
Subsection 25.6.2 Analyzing the connection
It is hard to overestimate the importance of the formula (25.6.1). Each piece comes from something inside-
First,
comes from the fact that we needed to apply this inversion, not just In fact, this particular inversion can be seen by integrating, as it's true thatso one can see that
and seem to correspond. Second, each
comes from each of the zeros of on the line in the complex plane. This is the part which most closely corresponds to the factoring.The constant term
comes from the constant when you do the factoring, similarly to the in the example above usingFinally, the integral in (25.6.1) comes from the zeros of
at we mentioned just before the statement of 25.3.7.
