Thank you. http://www.johndcook.com/blog/computing_binomial_coefficients/ This one from the link clarified.
On Mon, Apr 27, 2015 at 9:13 PM, Raul Miller <[email protected]> wrote: > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
