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
>>>>
>>>>
>>>>
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