Re: fourth degree equation

In article <euu96396u145kld9mvbqctiib3vbu58b1r@xxxxxxx>,
quasi <quasi@xxxxxxxx> wrote:

On Mon, 04 Jun 2007 23:52:51 -0500, Robert Israel
<israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

quasi <quasi@xxxxxxxx> writes:

On Mon, 04 Jun 2007 20:51:37 -0700, drc1@xxxxxxxxxxxx wrote:

What is the solution for x^4 - x + a = 0. (Solve for x in terms of a.)

It's not pretty.


Perhaps you'd find this series form pretty:

x = sum_{j=0}^infinity (4j choose j)/(3 j + 1) a^(3j+1)

Much better looking.

And possibly useful as well.

But does it work?

I tried it in Maple with a=-1 and also with a=-2. Neither value seemed
to work.

Can you give a numerical example?

Since 4 j choose j is going to infinity pretty fast,
I'd say that at the very least you need |a| < 1
for convergence.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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