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Re: InverseFunction[]

• To: mathgroup at smc.vnet.net
• Subject: [mg42160] Re: InverseFunction[]
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Sat, 21 Jun 2003 02:49:36 -0400 (EDT)
• Organization: The University of Western Australia
• References: <bbt23g$nj3$1@smc.vnet.net> <bc1jh1$bjp$1@smc.vnet.net> <200306110749.DAA02507@smc.vnet.net> <bc7pet$6f0$1@smc.vnet.net> <paul-000944.15584413062003@news.uwa.edu.au> <bcjv91$hv3$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <bcjv91$hv3$1 at smc.vnet.net>,
 Murray Eisenberg <murray at math.umass.edu> wrote:

> Well, to take the example of the function you pose for comparison, Sin: 
>   The section "Some Notes on Internal Implementation" in the Mathematica 
> Book's "Mathematica Reference Guide", says:
> 
>     Exponential and trigonometric functions use Taylor series,
>     stable recursion by argument doubling, and functional relations.
> 
> But I'm guilty of not scrolling down far enough on that same page to 
> have discovered:
> 
>    PolyLog uses Euler-Maclaurin summation, expansions in terms
>    of incomplete gamma functions and numerical quadrature.

PolyLog not ProductLog?

ProductLog uses high-order Newton's method starting from rational 
approximations and asymptotic expansions. 

> That's the sort of thing I was looking for and somehow had previously 
> overlooked!

So you were only interested in how Mathematica computes a function 
numerically? This was not clear from your original question:

> But what is the definition of the function as Mathematica knows it?

To me the definition of a function is not how it is computed numerically.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
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• Follow-Ups:
  • Re: Re: InverseFunction[]
    • From: Murray Eisenberg <murray@math.umass.edu>

• References:
  • Re: InverseFunction[]
    • From: Paul Abbott <paul@physics.uwa.edu.au>