sci.physics.relativity

Hannu Poropudas wrote:
[snip]

> I checked and result is that the series approximation of x^x above is
> NOT good:
>
> x ,bad series approx of x power x , x power x
>
> 63
> 34
> 04
> 75
> 48
> 24 79
> 05 37
> 92 10
> 87 00
> 92 11
> 10 45
> 42
> 91
> 59
> 50
>
>
>
>
>
> Hannu

I don't know how you got those results above. A simple 5 terms series
approximation with Maple V gives:

>series(x^x,x,5);

>p:=convert(",polynom);

>f:=unapply(p,x);

>g:=x->x^x;

> for n from to 2 by do
> print(n/10,f(n/10),g(n/10));
> od;
x series x^x x^x
.01000000000, .9549925877, .9549925860
.02000000000, .9247420604, .9247420362
.03000000000, .9001475185, .9001474129
.04000000000, .8791896003, .8791893115
.05000000000, .8608922723, .8608916593
.06000000000, .8446750111, .8446739002
.07000000000, .8301523617, .8301505554
.08000000000, .8170500145, .8170472996
.09000000000, .8051631665, .8051593227
.1000000000, .7943334282, .7943282347
.1100000000, .7844349521, .7844281951
.1200000000, .7753655887, .7753570668
.1300000000, .7670409759, .7670305041
.1400000000, .7593904360, .7593778496
.1500000000, .7523540384, .7523391964
.1600000000, .7458804431, .7458632294
.1700000000, .7399252788, .7399056040
.1800000000, .7344499018, .7344277040
.1900000000, .7294204308, .7293956756
.2000000000, .7248069838, .7247796637

Looks pretty good to me.
--
. Galidakis --- /