Roots of a Polynomial

Mechanics, discrete, statistics, ...
MuthuVeerappanR
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Roots of a Polynomial

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.

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MuthuVeerappanR
Posts: 348
Joined: Sun Mar 22, 2015 2:30 pm
Location: India
Contact:

Re: Roots of a Polynomial

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..

It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.