[AIS] (alternating) Iteration series: Half-iterate using the AIS?

[Gottfried]

Code:

{asumsine(x)=   5.5313086758882852195782696632367
+x^ 1* -2.0430674012650642389618054781319
+x^ 2* -0.37225775792009989386677189320438
+x^ 3*  0.099658659136533363777013664824123
(...)

Hi Sheldon -
I just crosschecked your function with my asum_hgh(x)-function:

Code:

h1 = 0.5
    x1 = asumsine(h1)
h_chk = asumhgh(x1)+1  \\ I'd centered h0 to be one period distant from asumsine(0)
h1 - h_chk
%1290 = 0E-125

perfect match! Extremely cool :-)

It's sunday, I'll come back to this perhaps in the evening. Thanks so far!

Gottfried