BTW, both Fricas and Mathematica give expressions whose derivatives numerically coincide with f(x) on the range (0..120), up to numerical noise. But I haven't been able to prove that those expressions (or their derivatives) are equal, nor than these derivattives are equal to f(x).
HTH, Le dimanche 25 août 2019 16:30:13 UTC+2, Emmanuel Charpentier a écrit : > > Indeed. But no need for Mathematica : > > sage: f(x)= sqrt(2+sqrt(2+sqrt(2+2*cos(5*sqrt(x)+4))))*x^(-1/2) > sage: h(x)= 2*cos(5/8*sqrt(x)+1/2)/sqrt(x) > sage: P1=plot(f(x),(x,0,120),ymin=-0.5, ymax=0.85) > sage: P2=plot(h(x),(x,0,120),ymin=-0.5, ymax=0.85) > sage: P1+P2 > > [image: tmp_a7yhgbnu.png] > > BTW: How did you came to exhume a 4-years old thread ? > > > Le samedi 24 août 2019 14:17:48 UTC+2, Rodrigo Sambade Saá a écrit : >> >> Dear William, >> >> Andrew is wrong >> <https://www.wolframalpha.com/input/?i=2*cos%285%2F8*sqrt%28x%29%2B1%2F2%29%2Fsqrt%28x%29+%3D+sqrt%282%2Bsqrt%282%2Bsqrt%282%2B2*cos%285*sqrt%28x%29%2B4%29%29%29%29*x%5E%28-1%2F2%29> >> . >> >> Best wishes, >> >> Rodrigo >> >> El jue., 12 feb. 2015 a las 21:57, William Stein (<wst...@gmail.com>) >> escribió: >> >>> On Thu, Feb 12, 2015 at 12:55 PM, R. Andrew Ohana >>> <andre...@gmail.com> wrote: >>> > It is wrong, but not as wrong as you make it out to be. Your function >>> is f = >>> > abs(h), where h = 2*cos(5/8*sqrt(x)+1/2)/sqrt(x). Rather that >>> integrating f, >>> > it seems to have integrated h. >>> >>> Andrew -- very good point! That's not nearly as bad as I made it out. >>> Thanks, >>> >>> -- William >>> >>> > >>> > -- >>> > You received this message because you are subscribed to the Google >>> Groups >>> > "sage-support" group. >>> > To unsubscribe from this group and stop receiving emails from it, send >>> an >>> > email to sage-s...@googlegroups.com. >>> > To post to this group, send email to sage-s...@googlegroups.com. >>> > Visit this group at http://groups.google.com/group/sage-support. >>> > For more options, visit https://groups.google.com/d/optout. >>> >>> >>> >>> -- >>> William (http://wstein.org) >>> >> -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/f471774a-faea-4bbc-8ef8-1c955fdfbee5%40googlegroups.com.
