And don't mistake easiness for unimportance. The solution is even easier than Henry chooses to present it...
m=. a,b n=. c That's all anyone needs to know in order to transfer a formula from A&S into J. That's all I was expecting to be told. Yet nobody did. Why not? Henry offers one answer. I have a different one. Neither of us will earn friends with our answers, so perhaps I'll keep my counsel. Let's just say this. H. is not a primitive J newcomers will tumble over themselves to use. But the way it's presented / documented / imparted is symptomatic of a wider problem with traditional math. We need to ask ourselves: is J the solution -- or part of the problem? On Sun, Jan 19, 2014 at 6:36 AM, Henry Rich <[email protected]> wrote: > Don't mistake indifference for disability. > > fixing the rank of z: > > > F=: 3 : 0 > 50 F y > : > NB. Convert F(a;b;c;z) into H. call > NB. x is number of terms of the series to sum > 'a b c'=: 3{.y > z=. > 3{y > m =. > 0 1 { y > n=. > 2 { y > x m H. n z > ) > > F 1;1;2;0.5 > 1.38629 > -@(% * ^.@-.) 0.5 > 1.38629 > > That's A&S 15.1.3. I'll have to take their word for the rest of them. > > Henry Rich > > > On 1/19/2014 12:27 AM, Ian Clark wrote: > >> Thanks Henry. >> >> I'll revise what I said: >> >> Including JfC, Concrete Math Companion, Vector, and Ewart Shaw's posting >> !! >> >> Here, to make it really, really easy, is a template to get you started... >> >> F=: 3 : 0 >> 50 F y >> : >> NB. Convert F(a;b;c;z) into H. call >> NB. x is number of terms of the series to sum >> 'a b c'=: 3{.y >> z=. > 3}.y >> m=. ?????????? >> n=. ?????????? >> x m H n z >> ) >> >> Why is it so ***** difficult for everyone to give me the answer I want? >> >> >> >> On Sun, Jan 19, 2014 at 5:15 AM, Henry Rich <[email protected]> wrote: >> >> JfC chapter 31 has a description of H. that I thought was pretty clear. >>> >>> Henry Rich >>> >>> >>> On 1/19/2014 12:08 AM, Ian Clark wrote: >>> >>> Okay, I know the answer now. But I dare anyone to discover it from the >>>> existing J Help documentation of (H.) ! >>>> >>>> Including Concrete Math Companion, Vector, and Ewart Shaw's posting !! >>>> >>>> Your mission, should you accept it, is to define a verb F that accepts >>>> an >>>> argument in (roughly) the syntax of Abramowitz and Stegun (A&S) chapter >>>> 15, >>>> viz F(a;b;c;z), and calls (H.) with the correct arguments. >>>> >>>> Here's some examples drawn from A&S... >>>> >>>> ln=: ^. >>>> arcsin=: _1&o. >>>> arctan=: _3&o. >>>> ] z=: 5%~ i.6 >>>> 0 0.2 0.4 0.6 0.8 1 >>>> >>>> F(1;1;2;z) NB. [15.1.3] >>>> -(ln 1-z)%z >>>> 0 1.11572 1.27706 1.52715 2.0118 _ >>>> >>>> F(1r2;1;3r2;z^2) NB. [15.1.4] >>>> -:(ln (1+z)%(1-z))%z >>>> 0 1.01366 1.05912 1.15525 1.37327 _ >>>> >>>> F(1r2;1;3r2;-z^2) NB. [15.1.5] >>>> (arctan z) %z >>>> 0 0.986978 0.951266 0.900699 0.843426 0.785398 >>>> >>>> F(1r2;1r2;3r2;z^2) NB. [15.1.6] >>>> (arcsin z) %z >>>> 0 1.00679 1.02879 1.0725 1.15912 1.5708 >>>> >>>> It's 4 instances of the Hypergeometric Series (F) with the functions it >>>> is >>>> supposed to approximate when 0<(|z)<1. (So for z=0 and z=1 the results >>>> can't be expected to match. But I've included these values in z anyway.) >>>> >>>> Hint: call H. with left argument x=50 (the number of terms of the series >>>> to >>>> be summed) as it can take a long time if you let it go to the limit by >>>> calling it monadically. >>>> >>>> Just to preempt someone splitting hairs, no my J syntax of A&S's >>>> F(a,b;c;z) >>>> isn't quite the same. A&S has a comma as the first separator, whereas >>>> I've >>>> a semicolon. >>>> >>>> IanClark >>>> >>>> >>>> >>>> >>>> >>>> On Sat, Jan 18, 2014 at 6:09 PM, Mike Day <[email protected]> >>>> wrote: >>>> >>>> Ewart Shaw wrote about these, so look for his emails on the subject >>>> >>>>> failing other channels. He might like to comment for himself, of >>>>> course, >>>>> if his e-address (as I have it, above) is still correct. >>>>> >>>>> Mike >>>>> >>>>> >>>>> On 18/01/2014 11:01, Ian Clark 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 >>>>>> >>>>>> >>>>>> >>>>>> --- >>>>> This email is free from viruses and malware because avast! Antivirus >>>>> protection is active. >>>>> http://www.avast.com >>>>> >>>>> >>>>> ---------------------------------------------------------------------- >>>>> 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 >>> >>> ---------------------------------------------------------------------- >> 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
