Cauchy Integral Experiment

[mike3]

You may take the ready-to-use alforithm at CZ,
http://en.citizendium.org/wiki/Legendre-...re_formula

there is an example of the implementation (and test with 32 digits) at
http://en.citizendium.org/wiki/GauLegExample/code

Hmm. Looks like it might be better. I might give it a try.

By the way, does your C++ compiler support the complex<long double> variables?
Then, perhaps, you could change to C++;
and in my codes, you may change the definition of z_type to complex<long double>

Not sure about that.

Did it take you by surprise?

Not so much: I saw it in my dream, sleeping, and in the morning I drew it with pensil and colored pens. Then I tried to calculate it. As you, I increased the precision gradually; so, the beauty of the God's gift revealed step by step. But still I do not understand: why the colleagues working on this problem during many generations did not see or did not accept this gift? You see, it is so easy...

So did you have some sort of intuitive idea as to what it might look like before you actually went and ran the equation?

As for why they didn't see it before, well the lack of powerful computers may have been a problem. In addition, I'm not sure if anyone knew the formula before, e.g. how would they have known that it decayed to the fixed points at imaginary infinity? I'm sort of curious as to how you figured it should do this yourself.