This might give a hint:
http://en.wikipedia.org/wiki/Figurate_number#Triangular_numbers
On 2015-04-27 15:09, June Kim (김창준) wrote:
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 ?
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