Question: How to get Maple to display a closed-form expression (if available)?

How do I get a closed-form expression?

I tried the following (e.g.):


> k[21] := t-> piecewise(t<0,0,p*(1-p)^t);                      {definition of descrete probability distribution, here: geometric distribution}

> u2 := t-> log(t);                                                           {definition of utility function, here: DARA (decreasing absolute risk aversion)}

> E[21,2] := sum( k[21](t) * u2(t), t=-infinity..infinity);    {definition of expected utility}

> eqn[21,2] := u2(s) = E[21,2];                                      {utility function gets equalized to expected utility}

> solve( eqn[21,2], s);                                                   {solve equation above for s, to get the certainty equivalent}


This is just an example. I tried this procedure for a lot of utilitys and probability distributions but did not receive a single closed-form exprssion.

I already know, that maple usually defines variables as complex numbers, so I assumed for all used variables a range within the real numbers.

It may be, that some solutions do not have a cosed-form expression, but I´ll need to be sure and try everything possible to find a closed-form expression if there is one.

May someone help me?

I would also be glad to get some tipps how to simplify solutions or take other ways to receive closed-form expressions or even for links where I can read about possibilities to simplify solutions to closed-fom expressions.

Thank you very much for every help you can give me!

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