Maple V.4 gave the first few terms of the asymptotic expansion of a hypergeometric function correctly (albeit without the O(something) term):

|\^/| Maple V Release 4 (Victoria University)
._|\| |/|_. Copyright (c) 1981-1996 by Waterloo Maple Inc. All rights
\ MAPLE / reserved. Maple and Maple V are registered trademarks of
<____ ____> Waterloo Maple Inc.
| Type ? for help.

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?

|\^/| Maple 2015 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2015
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.

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.)

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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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