[math-fun] Sequence of polynomials with largest real root approaching e?
Is there a sequence of polynomials p_n(x) such that p_n(x) is degree n p_{n+1}(x) = p_n(x) + k_n and the largest root of p_n approaches e as n -> infinity? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Oops! k_n should be an integer. On Tue, Apr 16, 2013 at 8:56 AM, Mike Stay <metaweta@gmail.com> wrote:
Is there a sequence of polynomials p_n(x) such that
p_n(x) is degree n p_{n+1}(x) = p_n(x) + k_n
and the largest root of p_n approaches e as n -> infinity? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Do you mean p_{n+1}(x) = x * p_n(x) ? On 2013-04-16 10:57, Mike Stay wrote:
Oops! k_n should be an integer.
On Tue, Apr 16, 2013 at 8:56 AM, Mike Stay <metaweta@gmail.com> wrote:
Is there a sequence of polynomials p_n(x) such that
p_n(x) is degree n p_{n+1}(x) = p_n(x) + k_n
and the largest root of p_n approaches e as n -> infinity? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Gah, let me try again: 1. p_n(x) is degree n 2. p_{n+1}(x) = x * p_n(x) + k_n, where k_n is an integer 3. Largest real roots approach e as n -> infinity. On Tue, Apr 16, 2013 at 9:34 AM, Mike Speciner <ms@alum.mit.edu> wrote:
Do you mean p_{n+1}(x) = x * p_n(x) ?
On 2013-04-16 10:57, Mike Stay wrote:
Oops! k_n should be an integer.
On Tue, Apr 16, 2013 at 8:56 AM, Mike Stay <metaweta@gmail.com> wrote:
Is there a sequence of polynomials p_n(x) such that
p_n(x) is degree n p_{n+1}(x) = p_n(x) + k_n
and the largest root of p_n approaches e as n -> infinity? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
participants (2)
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Mike Speciner -
Mike Stay