**TI92P*mainSingle file dated Mon Oct 23 11:16:51 20ReulersumR¥Zø(z)
Func
© Version 2023/10/23
© Copyright 2023 John Scott (https://johnscott.me)
© This program is free software subject to the GNU General Public License as published by the Free Software Foundation, either version three of the license or, at your option, any later version.
© This teeny function performs Euler summation, also known as the Euler transform (not to be confused with the Euler-Maclaurin summation formula). It is primarily used for alternating and Fourier series and does a terrific job accelerating the convergence of such series in an efficient way. It also is a way of accomplishing analytic continuation and sums divergent series with the expected results most of the time.
© To actually use this function, pass some series terms as a list. In practice, it's often beneficial to sum some terms manually first and then pass the rest to the Euler transform.
Local s
0s
Local k,c
dim(z)c
For k,1,c
s+2^(k)*z[1]s
seq(z[w]+z[w+1],w,1,dim(z)-1)z
EndFor
Return s
EndFuncäåÜ¨c