Bill Allombert on Sat, 08 Mar 2014 18:21:57 +0100

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Re: Is it normal intnumromb to not return result in more than 90 minutes?

On Sat, Mar 08, 2014 at 04:29:46PM +0200, Georgi Guninski wrote:
> This code doesn't return result in at least
> 90 minutes and I interrupted it.
> f1(x)=1/2+I/(2*Pi)*log(-exp(-2*Pi*I*x));
> P(x)=f1((gamma(x)+1) /x);
> intcircromb(a,b,f)=intnumromb(t=0,2*Pi,f(a+b*exp(I*t))*exp(I*t))/2/Pi*b;
> my(f(x)=P'(x)/P(x));intcircromb(3,2.5,f)
> Is this normal?

Unfortunately yes, intnumromb and gamma are slow. You can speed things
up by using \p9 on a 32-bit system.

> And is P(x) meromorphic?

Not when using a fixed determination of log().
If you replace log(-exp(-2*Pi*I*x)) by (-2*Pi*I*x+I*Pi)
then yes, but it is probably not what you want.