Closed Form

[dan_h]

When I tried the integral of x^3/exp(x)-1 from zero to infinity, as mentioned in other posts, the Prime didn't process it. That made me think it couldn't find a closed form.

Per my Harper Collins math dictionary, a closed form is an expression for a function or quantity, especially an integral, in terms of known and well understood quantities. It gives an example, the integral of exp(-x^2) from negative to positive infinity yielding the square root of Pi.

On the Prime, doing this from zero to infinity, it yields 1/2 the square root of Pi.

On my HP Pavilion, I have the Home Edition of Mathematica 9. It was able to handle the integral of x^3/exp(x)-1 from zero to infinity and yielded 1/15 Pi^4.

Maybe in time future updates to the Prime will be able to find more "closed forms."