| Hypergeometric functions [message #27519] |
Wed, 24 October 2001 00:37  |
Ralf Flicker
Messages: 19
Registered: October 2001
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Junior Member |
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Does anybody know of an available IDL implementation for
generalized hypergeometric functions ? I need in particular
2F3(a,b;c,d,e;z^2), which is absolutely convergent for all real
z. I can't seem to find anything among the standard sources, but
thought I'd check here before I start coding it myself.
ralf
--
Ralf Flicker UIN : 65334076
Gemini Observatory http://www.gemini.edu/
670 N. A'Ohoku Pl. Tel : (808) 974-2569
Hilo 96720, HI, USA Fax : (808) 935-9235
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| Re: Hypergeometric functions [message #27637 is a reply to message #27519] |
Tue, 30 October 2001 07:24  |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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colinr@toliman.uio.no (Colin Rosenthal) writes:
> On Mon, 29 Oct 2001 20:34:17 -1000,
> Ralf Flicker <rflicker@gemini.edu> wrote:
>
>> Yes, that's what I ended up doing, and it works fine. I realize
>> the function is somewhat special (the only substantial reference
>> to 2F3 that I could find on the web was to a Mathematica
>> implementation), but I was partly fishing for information in
>> general about these kinds of special functions. As you say, IDL
>> is a mite weak on this point.
>
> There's a book by Slater which contains formulae for asymptotic expansions
> etc. of hypergeomtric functions. The book is called, fascinatingly
> enough, "Hypergeometric Functions" and is a rip-roaring read. If you
> find yourself enthralled by the lyricism of her chapter on integral
> representations, may I recommend her thrilling sequel "Confluent Hypergeometric
> Functions"?
I cried in the fourth chapter. (sniff)
Craig
--
------------------------------------------------------------ --------------
Craig B. Markwardt, Ph.D. EMAIL: craigmnet@cow.physics.wisc.edu
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
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| Re: Hypergeometric functions [message #27643 is a reply to message #27519] |
Tue, 30 October 2001 01:53 |
colinr
Messages: 30
Registered: July 1999
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Member |
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On Mon, 29 Oct 2001 20:34:17 -1000,
Ralf Flicker <rflicker@gemini.edu> wrote:
> Yes, that's what I ended up doing, and it works fine. I realize
> the function is somewhat special (the only substantial reference
> to 2F3 that I could find on the web was to a Mathematica
> implementation), but I was partly fishing for information in
> general about these kinds of special functions. As you say, IDL
> is a mite weak on this point.
There's a book by Slater which contains formulae for asymptotic expansions
etc. of hypergeomtric functions. The book is called, fascinatingly
enough, "Hypergeometric Functions" and is a rip-roaring read. If you
find yourself enthralled by the lyricism of her chapter on integral
representations, may I recommend her thrilling sequel "Confluent Hypergeometric
Functions"?
--
Colin Rosenthal
Astrophysics Institute
University of Oslo
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| Re: Hypergeometric functions [message #27645 is a reply to message #27519] |
Mon, 29 October 2001 22:34 |
Ralf Flicker
Messages: 19
Registered: October 2001
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Junior Member |
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Craig Markwardt wrote:
>
> Ralf Flicker <rflicker@gemini.edu> writes:
>
>> Does anybody know of an available IDL implementation for
>> generalized hypergeometric functions ? I need in particular
>> 2F3(a,b;c,d,e;z^2), which is absolutely convergent for all real
>> z. I can't seem to find anything among the standard sources, but
>> thought I'd check here before I start coding it myself.
>
> Hi Ralf--
>
> I see you haven't gotten a response to this question for the past
> several days. I think the answer is that IDL is pretty weak on
> special functions, although it does have a few.
>
> However, the particular hypergeometric function you are seeking is
> rather esoteric. I cannot find it in the GNU scientific library, nor
> in CEPHES. These are two C libraries of special functions. [ Nor,
> for that matter, can I find it cursorily in Abramowitz & Stegun. ] It
> looks like you will have to code this yourself.
>
> If it's really convergent then it should be rather simple to code the
> series directly.
Yes, that's what I ended up doing, and it works fine. I realize
the function is somewhat special (the only substantial reference
to 2F3 that I could find on the web was to a Mathematica
implementation), but I was partly fishing for information in
general about these kinds of special functions. As you say, IDL
is a mite weak on this point.
ralf
--
Ralf Flicker UIN : 65334076
Gemini Observatory http://www.gemini.edu/
670 N. A'Ohoku Pl. Tel : (808) 974-2569
Hilo 96720, HI, USA Fax : (808) 935-9235
|
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| Re: Hypergeometric functions [message #27649 is a reply to message #27519] |
Mon, 29 October 2001 19:47 |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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Ralf Flicker <rflicker@gemini.edu> writes:
> Does anybody know of an available IDL implementation for
> generalized hypergeometric functions ? I need in particular
> 2F3(a,b;c,d,e;z^2), which is absolutely convergent for all real
> z. I can't seem to find anything among the standard sources, but
> thought I'd check here before I start coding it myself.
Hi Ralf--
I see you haven't gotten a response to this question for the past
several days. I think the answer is that IDL is pretty weak on
special functions, although it does have a few.
However, the particular hypergeometric function you are seeking is
rather esoteric. I cannot find it in the GNU scientific library, nor
in CEPHES. These are two C libraries of special functions. [ Nor,
for that matter, can I find it cursorily in Abramowitz & Stegun. ] It
looks like you will have to code this yourself.
If it's really convergent then it should be rather simple to code the
series directly.
Craig
--
------------------------------------------------------------ --------------
Craig B. Markwardt, Ph.D. EMAIL: craigmnet@cow.physics.wisc.edu
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
------------------------------------------------------------ --------------
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