http://www.jsoftware.com/jwiki/Vocabulary/bang#dyadic now has a reference to http://www.johndcook.com/blog/binomial_coefficients/ - does that help at all?
Thanks, -- Raul On Mon, Apr 27, 2015 at 7:50 AM, June Kim (김창준) <[email protected]> wrote: > Well, it is embarassing but it seems like I forgot what I learned 8 years > ago. > > http://jsoftware.com/pipermail/programming/2009-July/015308.html > > It looks like the APL's Binomial and J's Out of have the same behavioral > model. > > On Mon, Apr 27, 2015 at 8:19 PM, June Kim (김창준) <[email protected]> wrote: > >> Hello >> >> I am translating Iverson's Notation as a Tool of Thought -- it is too be >> published in a book called Great Papers in Computer Science in Korean. >> >> Reading the paper, I have a question about "binomial"(!). This mailing >> list is of course about J, but I find this place very friendly and the >> people here widely informed, I post it here. >> >> First, look at the passage from the paper: >> >> The symbol ! denotes the binomial coefficient function, and the table >>> d∘.!d is seen to contain Pascal’s triangle with its apex at the left; >>> if extended to negative arguments (as with d←¯3 ¯2 ¯1 0 1 2 3) it will >>> be seen to contain the triangular and higher-order figurate numbers as well. >> >> >> So the author means the outer product of binomial of _3 _2 _1 0 1 2 3 >> contains figurate numbers. However, after looking up many manuals for >> various versions of APL I couldn't find out clear descriptions for when the >> arguments are negative(or one is negative and the other positive). I looked >> up J dictionary and it didn't have clear definition for this case, either. >> >> Could anyone please help me out understanding what d∘.!d do with >> d←¯3 ¯2 ¯1 0 1 2 3 ? >> >> >> > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
