Mon Sep 24 16:14:26 EEST 2018

Math challenge of the day 2018-09-24


Math challenge of the day 2018-09-24

For complex $x$ define 

f(x)=exp(x^2)-exp(x)-1

Is it true that f(5 i pi) = 0?

We have strong numerical evidence with precision
100 decimal digits but some meromorphic doubts too ;)

gp/pari session (warning, gp is very buggy):

parisize = 8000000, primelimit = 500000, nbthreads = 2
? \p 100
   realprecision = 115 significant digits (100 digits displayed)
? f(x)=exp(x^2)-exp(x)-1
%1 = (x)->exp(x^2)-exp(x)-1
? f(5*I*Pi)
%2 = 6.952351934431877974 E-108 + 0.E-114*I

Cheers for the day.

Posted by cheers | Permanent link