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meymathis · #2 December 11th, 2008, 10:59 AM

$\int^{x}_{-\infty}a\exp(-|b t|^c)\, dt$

After some googling, I have not found anything better than that.

You can write down the expression in terms of the generalized error function (see this) but in the end you still have the same integral at the heart of it. The fact is that you cannot find an expression that doesn't contain either an integral or an infinite series for the general case. For certain values of c (like 1), you could obviously write down a closed form expression (though I think it might have to have to be broken up into 2 expressions, one if $x<0$ and one for $x\geq 0$ )

Even if you look at c=2, which is Gaussian (see this) they write the CDF in terms of the error function which is an integral expression.