I was able to reproduce, not without some difficulties, the first couple of
tables in that page following a pedestrian approach; but apparently there
is a (theoretical based?) shortcut to define the gs function (see
https://tromp.github.io/pearls.html ). Maybe, one of the Haskell literate
members of the forum can transcribe it to J.
If still of interest. Here's a J version:
S=: 1 :0
:
if. 0= y do. 0
else. 'q r'=. (0,m) #: y
( r *(1+m) ^ (0 (m S) x)) + (1+x) m S q
end.
)
G=: (>:@[ $: _1+ 4 : '0 (x S)y')`[@.(0=])
e.g.
2 G"0 i.4
2 3 5 7
3 G"0 i.13
3 4 5 7 9 11 15 19 23 63 159 383 2047
As an aside: in general n G i.k
can be replaced for the first n^2 terms with
Gdiff=:+/\@(,}.@($~#2^i.))
e.g.
Gdiff 3
3 4 5 7 9 11 15 19 23
-Arie
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