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Roots of a Polynomial

Posted: Tue Jan 09, 2018 10:17 am
by MuthuVeerappanR
Is there a general expression to find the roots of the following polynomial?

$z^n + n z^{n - 1} + n(n - 1)z^{n - 2} + n(n - 1)(n - 2)z^{n - 3} + \cdots + n! = 0$?

The structure of the polynomial seems to suggest there can be something that can be done to evaluate the roots explicitly but I can't see it. Any help? Thanks.

Re: Roots of a Polynomial

Posted: Tue Jan 09, 2018 12:56 pm
by MuthuVeerappanR
Okay, the above equation reduces to the truncated exponential which can alternately written as the Incomplete Gamma function. And the following post says there is no known simple expression.

Roots of the incomplete Gamma function

Thanks all..