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.
Roots of a Polynomial

 Posts: 419
 Joined: Sun Mar 22, 2015 2:30 pm
 Location: India
 Contact:
Roots of a Polynomial
It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.

 Posts: 419
 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..
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.
Re: Roots of a Polynomial
I completely agree with you.MuthuVeerappanR wrote: ↑Tue Jan 09, 2018 12:56 pmOkay, 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..