       some abnormalities

• To: mathgroup at smc.vnet.net
• Subject: [mg8218] some abnormalities
• From: Wouter Meeussen <w.meeussen.vdmcc at vandemoortele.be>
• Date: Tue, 19 Aug 1997 21:11:57 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```hi folks:

some abnormalities to check out on other platforms.
If you find different behaviour, please tell me.
In particular, give Mma 3.0.1 a go at it.

my system: Compaq prolinea 590, (90MHz, 48Mb, Win NT 3.51 sp4)
running Mma 3.0.

note the 2 following curiosities:
1/	line In only simplifies to integers up to n=11,
bigger n are left unsimplified

2/	RSolve gives a symbolic solution that does not agree
with what it should be numerically (see last line).

what is wrong?
------------------------------------------------------------

In:=
<<DiscreteMath`RSolve`
In:=
it=RSolve[{ a[n] == a[n-1] -Binomial[3n,2n]+Binomial[2n,n],
a == 1}, a[n], n]
NRoots::eqn: DiscreteMath`RSolve`Private`nST - 1. K[1.] == 0 is not an
equation.
Out=
-I
{{a[n] -> ------- -
Sqrt

1 + n       3                            3
4      Gamma[- + n] HypergeometricPFQ[{1, - + n}, {2 + n}, 4]
2                            2
-------------------------------------------------------------}}
Sqrt[Pi] Gamma[2 + n]
In:=
st=FullSimplify[a[n]/.it]
Out=
3
Gamma[3 + 2 n] Hypergeometric2F1Regularized[1, - + n, 2 + n, 4]
-I                                                     2
{------- - ---------------------------------------------------------------}
Sqrt                            Gamma[2 + n]
In:=
Table[st//Simplify,{n,13}]//Flatten
Out=
{3, 9, 29, 99, 351, 1275, 4707, 17577, 66197,

-I                                   23
------- - 705432 HypergeometricPFQ[{1, --}, {12}, 4],
Sqrt                                2

-I                                    25
------- - 2704156 HypergeometricPFQ[{1, --}, {13}, 4],
Sqrt                                 2

-I                                     27
------- - 10400600 HypergeometricPFQ[{1, --}, {14}, 4],
Sqrt                                  2

-I                                     29
------- - 40116600 HypergeometricPFQ[{1, --}, {15}, 4]}
Sqrt                                  2

what it should be is:

b[n_]:=b[n]= b[n-1] -Binomial[3n,2n]+Binomial[2n,n]; b:= 1

Table[b[n],{n,13}]

{0, -9, -73, -498, -3249, -20889, -133737, -856338, -5494543, -35354802,

-228186090, -1477159634, -9589184478}

baffled as always,

wouter.

NV Vandemoortele Coordination Center
Oils & Fats Applied Research
Prins Albertlaan 79
Postbus 40
B-8870 Izegem (Belgium)
Tel: +/32/51/33 21 11
Fax: +/32/51/33 21 75
vdmcc at vandemoortele.be

```

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