Thank you so much! You'll see I did post a couple of responses earlier but I now realize I was replying to myself instead of to you). When I first read your guidance I thought I would inevitably have to come back to ask for more help. But in fact, with very slow and careful work following your...
First steps, which I hope I have right. Evaluate ##F(0)## ...
Recognize that:
##f_k## involves the product of a ##\mathrm{sinc}## function and an exponential.
Once we set ##t=0##, the ##\mathrm{sinc}## function reduces to ##\mathrm{sinc}(\pi k)##
The summation variable ##k## is always an...
Now that I've been working on it, I see that there is something I didn't notice at first; something I realise I don't understand.
Please could you explain why the exponent of the ##F(0)## term in the second line of the identity
\begin{split}
F'(0) &= n\left(\sum_{k=-\infty}^\infty...
Problem summary
I have the characteristic function of a probability distribution but I'm having difficulty obtaining its derivative.
Background
I am reading the following paper: Schwartz, Lowell M. (1980). On round-off error. Analytical Chemistry, 52(7), 1141-1147. DOI:10.1021/ac50057a033.
The...