       • To: mathgroup at smc.vnet.net
• Subject: [mg25934] Re: [mg25918] S.O.S. , please......
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Thu, 9 Nov 2000 03:04:30 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```You shoudl really learn to use proper Mathematica notation. Your definition
should have been:

y[R_] := A*(R^b)*Exp[-c*R]

Using Solve, PowerExpand and FullSimplify a few times I got the following
expressions for {A,b,c}:

In:=
{A, b, c}

Out= {E^((r0*(r0*y1^2 - y0*(y1 + r0*y2)))/y0^2)*r0^((r0^2*(-y1^2 +
y0*y2))/y0^2)*y0,
(r0^2*(y1^2 - y0*y2))/y0^2,
((r0^2*(y1^2 - y0*y2)*Log[r0])/y0^2 - Log[y0] + Log[E^((r0*(r0*y1^2 - y0*(y1
+ r0*y2)))/y0^2)*r0^((r0^2*(-y1^2 + y0*y2))/y0^2)* y0])/r0}

We can check that it works under those conditions when PowerExpand is valid:

In:=
y[r0] // PowerExpand // FullSimplify

Out=
y0

In:=
y'[r0] // PowerExpand // FullSimplify

Out=
y1

In:=
y''[r0] // PowerExpand // FullSimplify

Out=
y2

We can also check that it works for at least some values of {r0,y0,y1,y2}

In:=
{r0, y0, y1, y2} = Table[Random[], {4}]

Out=
{0.0991165, 0.327478, 0.0111691, 0.680594}

In:=
{y[r0], y'[r0], y''[r0]} == {y0, y1, y2}

Out=
True

on 00.11.8 1:05 PM, alessandro agresti at agresti at dffs.unifi.it wrote:

> I have the following function:
>
> y(R) =  A * [R^b] * [exp(-cR)]
>
> I know   y0=y(r_0),  y1=y ' (r_0),  y2=y " (r_0),  where r_0 is know value.
>
> Can anybody tell me if:
>
> 1) mathematica can help me to find the analitic formulas  for  the
> parameters : A,  b,  c
> 2) if yes , please tell me which are the commands to give Mathematica.
> 3) perhaps the better thing for me it is to receive the analitic formulas by
> e-mail;
> but I don't dare to hope it...........
>
> Thanks for Your BIG help.
>
> alessandro agresti
> e-mail: agresti at dffs.unifi.it
>
>
>

--
Andrzej Kozlowski
Toyama International University
JAPAN

http://platon.c.u-tokyo.ac.jp/andrzej/
http://sigma.tuins.ac.jp/

```

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