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Re: asympt(hypergeometric...)

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On 23.08.2016 06:14, jfh wrote:
> Maple V.4 gave the first few terms of the asymptotic expansion of a hypergeometric function correctly (albeit without the O(something) term):
>
...
>> readlib(hypergeom);
>                                proc()  ...  end
>
>> asympt(hypergeom([1],[3/2],x),x);
> bytes used=1000064, alloc=851812, time=0.75
>             1/2      1/2                         1          1     15  1
>       1/2 Pi    (1/x)    exp(x) - 1/2 1/x + 1/4 ---- - 3/8 ---- + --
> ----
>                                                   2          3    16   4
>                                                  x          x         x
> but now Maple 2015 can't to do it! Why is it worse than it was 19 years ago?
>
...
>> asympt(hypergeom([1],[3/2],x),x);
> Error, (in asympt) unable to compute series
>
> (Of course simplify will work around that problem, but more complicated cases like
hypergeom([1], [3/2, 3/2], x) do not reduce to simpler functions, though the necessary
mathematics to find their asymptotic series has been known since 1940 and involves just
the sort of calculation that Maple ought to be good at.)
>

Maple 2016 can do both, see below.

I want to encourage you to ask at the active Maple forum, http://www.mapleprimes.com/recent/all


hypergeom([1],[3/2],x);
asympt(%,x);

1/2*Pi^(1/2)*(1/x)^(1/2)*exp(x)-1/2/x+1/4/x^2-3/8/x^3+15/16/x^4-105/32/x^5+O(1/x^6)

hypergeom([1], [3/2, 3/2], x);
asympt(%,x);

(1/8*Pi^(1/2)*(1/x)^(3/4)+1/128*Pi^(1/2)*(1/x)^(5/4)+9/4096*Pi^(1/2)*(1/x)^(7/4)+75/65536*
Pi^(1/2)*(1/x)^(9/4)+3675/4194304*Pi^(1/2)*(1/x)^(11/4)+59535/67108864*Pi^(1/2)*(1/x)^(13/4)
+O((1/x)^(15/4)))*exp(2/(1/x)^(1/2))

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asympt(hypergeometric...) jfh <john.harper@vuw.ac.nz> - 2016-08-22 21:14 -0700
  Re: asympt(hypergeometric...) Axel Vogt <//noreply@axelvogt.de> - 2016-08-23 09:22 +0200

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