< 1095984862 0 :calamari_!Jeffry@dialup-4.240.108.185.Dial1.Phoenix1.Level3.net JOIN :#esoteric < 1095990385 0 :calamari-!Jeffry@dialup-4.240.111.230.Dial1.Phoenix1.Level3.net JOIN :#esoteric < 1095990951 0 :calamari_!unknown@unknown.invalid QUIT :Read error: 104 (Connection reset by peer) < 1095993288 0 :calamari-!unknown@unknown.invalid QUIT :Read error: 110 (Connection timed out) < 1095993326 0 :calamari-!Jeffry@dialup-4.240.111.230.Dial1.Phoenix1.Level3.net JOIN :#esoteric < 1095994756 0 :calamari-!unknown@unknown.invalid QUIT :"Leaving" < 1095995832 0 :calamari_!Jeffry@dialup-4.240.108.74.Dial1.Phoenix1.Level3.net JOIN :#esoteric < 1095996702 0 :calamari-!Jeffry@dialup-4.240.108.74.Dial1.Phoenix1.Level3.net JOIN :#esoteric < 1095996766 0 :calamari_!unknown@unknown.invalid QUIT :Read error: 104 (Connection reset by peer) < 1096007953 0 :calamari-!unknown@unknown.invalid PART #esoteric :? < 1096012799 0 :clog!unknown@unknown.invalid QUIT :ended < 1096012800 0 :clog!unknown@unknown.invalid JOIN :#esoteric < 1096055728 0 :fizzie!unknown@unknown.invalid PRIVMSG #esoteric :ho-hum. < 1096055744 0 :fizzie!unknown@unknown.invalid PRIVMSG #esoteric :well, now I have the solution for my last-evening function. < 1096055752 0 :lindi-!unknown@unknown.invalid PRIVMSG #esoteric :congrats :) < 1096055770 0 :fizzie!unknown@unknown.invalid PRIVMSG #esoteric :considering that I got it from the course assistant, I don't think it warrants congratulations. < 1096055886 0 :fizzie!unknown@unknown.invalid PRIVMSG #esoteric :the official way to solve it was to look at the function "u(z) = f(z) + z^3 - 3z", which is analytic and differentiable everywhere f(z) is, and that particular function makes f(z) simplify a bit, so that it is possible for a normal human to just look at lim_h->0 (u(z+h)-u(z))/h. < 1096055911 0 :fizzie!unknown@unknown.invalid PRIVMSG #esoteric :maybe 'u' was an unfortunate name. < 1096056018 0 :fizzie!unknown@unknown.invalid PRIVMSG #esoteric :and apparently also if the component functions u(z) and v(z) (when f(z) = u(z)+iv(z)) are differentiable and satisfy the cauchy-riemann equations in a single point, the function is indeed complex-differentiable there. it is a sufficient condition, but we weren't quite sure if it's a necessary one, too. < 1096056066 0 :fizzie!unknown@unknown.invalid PRIVMSG #esoteric :if the latter, it can be used to show that f(z) is complex-differentiable on the coordinate axes and analytic nowhere. < 1096056069 0 :fizzie!unknown@unknown.invalid PRIVMSG #esoteric :phew. < 1096056115 0 :lindi-!unknown@unknown.invalid PRIVMSG #esoteric :mm