### Mathematica

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• Fractal Friar
• Posts: 103

#### Mathematica

« on: November 25, 2017, 10:59:28 AM »
Hi

I do not have Mathematica. I look for otput of the :
Series[MandelbrotSetBoettcher[z], {z, \[Infinity], 5}]

or more if it is possible

See:
* http://reference.wolfram.com/language/ref/MandelbrotSetBoettcher.html

TIA

• 3c
• Posts: 826

#### Re: Mathematica

« Reply #1 on: November 26, 2017, 01:57:23 PM »
https://lab.open.wolframcloud.com/app/ has gratis online Mathematica notebooks, your code outputs this:
Code: [Select]
z+1/2-1/(8 z)+5/(16 z^2)-53/(128 z^3)+127/(256 z^4)-677/(1024 z^5)+O[1/z]^6

• Fractal Friar
• Posts: 103

#### Re: Mathematica

« Reply #2 on: November 26, 2017, 04:38:32 PM »
Thx. It works

Series[MandelbrotSetBoettcher[z], {z, \[Infinity], 10}]

z+ 1/2 - 1/8z + 5/16z^2 - 53/128z^3 + 127/256z^4 - 677/1024z^5 + 2221/2048z^6
- 61133/32768z^7 + 205563/65536z^8 - 1394207/262144z^9 + 4852339/524288z^10
+ O[1/z]^11

Does  O[1/z]^11 in big O-notation means that if one gest closer to Mandelbrot set ( |z|<1) that error will be greater ?

• 3f
• Posts: 1480

#### Re: Mathematica

« Reply #3 on: November 30, 2017, 04:30:52 AM »
Does  O[1/z]^11 in big O-notation means that if one gest closer to Mandelbrot set ( |z|<1) that error will be greater ?
It means the error is C/|z|^11 for some (unknown) constant C, so yes.

This paper (which is actually an explanation of another paper) discussed the series and how it's derived:
https://sites.math.washington.edu/~morrow/336_14/papers/alain.pdf