HP49-50G plotting of sum(x=0 to 0, 1, 2,...10, of x!/(2x)!)

[Thomas Klemm]

(11-05-2023 10:39 PM)Gil Wrote:  forgetting the square at the numerator,

I was already wondering why that square was in the code.

This is probably not much better than your solution:

Code:

\<< CL\GS 0 0 11
    FOR i
        i ! SQ
        2 i * ! / +
        DUP \GS+
    NEXT
\>>

And then I used the BAR plot.
This works with an HP-48GX.

---

For Sum[(k!)^2/(2k)!, k] the result is:

\[
\begin{align}
\sum_{k=0}^\infty \frac{(k!)^2}{(2 k)!}
= \frac{2}{27} \left(18 + \sqrt{3} \pi \right)
\approx 1.73639985871872
\end{align}
\]