Hi Ian - Ken Iverson's Concrete Math Companion, http://www.jsoftware.com/books/pdf/cmc.pdf, has 2 pages dedicated to it starting on page 59. I am too rusty on this level of math to comment on how well it describes it. It makes some sense and seems pretty clear.
GKP5.76 defines the hypergeometric as a sum over the products of two lists for all k not less than zero. The first list is the quotient of products over the rising factorials of two list parameters denoted by a and b, and the second is the powers of the argument z divided by corresponding factorials. To confine the matter to finite lists, we will introduce a further argument t, and treat only the values of k specified by i. t. The definitions will be used in the form t a hy b z, where hy is a conjunction. Thus: The primitive hypergeometric conjunction H. produces a rank-0 dyadic function equivalent to a hy b, and a monadic case that is its limit for an unlimited number of terms. For example: I particularly like how the CMC shows tests cases between the full definition and H. (10) 1 hy 1 " 0 i. 6 1 2.71828 7.38871 20.0634 54.1541 143.689 10 '' H. '' i. 6 1 2.71828 7.38871 20.0634 54.1541 143.689 Between wikipedia[1] and the Concrete Math Companion, I could probably figure it out, but not this early on a Saturday without coffee yet. Hope it helps in some way or perhaps triggers thoughts for others to contribute [1] - http://en.wikipedia.org/wiki/Hypergeometric_function On Sat, Jan 18, 2014 at 6:01 AM, Ian Clark <[email protected]> wrote: > Just one empty stub remains in the Accessible Dictionary (aka NuVoc > --remember it?): > > H. (Hypergeometric) Conjunction > http://www.jsoftware.com/jwiki/Vocabulary/hcapdot > > Once that's filled-in, then NuVoc is more-or-less ready to go. You can > already see it at http://www.jsoftware.com/jwiki/Vocabulary > But alas, I need help... > > The J Dictionary (the old one) references Abramowitz and Stegun (A&S), > Chapter 15: Hypergeometric Functions. Now A&S represent the syntax of the > general case like so: > > F(a; b; c; z) > > Both NuVoc and the J Dictionary present the syntax of the (H.) primitive > like so: > > (m H. n) y > > where both m and n are numeric lists. > > Now suppose I'm a newbie, and my first sight of: > http://www.jsoftware.com/help/dictionary/dhcapdot.htm > just gives me a dull ache between the eyes. I need clear, unambiguous > instructions for taking any example I choose from A&S and mapping it onto: > (m H. n)y > > Let me make a start: > z --> y > That was the easy bit. Now... how should (a; b; c) --> (m; n)? > > Or should I be asking: how *best* should (a; b; c) be mapped onto m and n? > Because as I see it, it's ambiguous. Just for starters: > > F(a; b; c; z) = F(b; a; c; z) -----[A&S 15.1.1] > > Suggestions please. > > IanClark > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
