Integration is not as easy as differentiation. From Mathematica: In[3]:= Integrate[Log[1-x]/x,x] Out[3]= -PolyLog[2,x]
On Fri, Jan 15, 2021 at 2:25 PM Devon McCormick <[email protected]> wrote: > The tacit form does not help with my anti-derivative attempt: > > (^.@-. % ]) deriv_jcalculus_ _1 > |domain error: deriv_jcalculus_ > | 13!:8(3) > |deriv_jcalculus_[:16] > > > On Fri, Jan 15, 2021 at 2:16 PM Henry Rich <[email protected]> wrote: > > > Right, you'll never get a closed-form derivative for an explicit > > function. Make it tacit: > > > > (^.@-. % ]) deriv_jcalculus_ 1 > > (((_1 * %@-.) * ]) - ^.@-. * 1"0) % *:@] > > > > The cases that are Lebesgue-integrable but not Riemann-integrable have > > discontinuities or infinities that are inconsistent with digital > > approximation, IIUC. > > > > Henry Rich > > > > On 1/15/2021 1:58 PM, Devon McCormick wrote: > > > The Lebesgue method is supposed to handle cases Riemann cannot. > > > I tried using the anti-derivatives from the calculus add-ons but cannot > > > make them work for an arbitrary user-defined function like "f3=: ] %~ > [: > > ^. > > > -.". > > > > > > On Fri, Jan 15, 2021 at 9:16 AM 'Pascal Jasmin' via Programming < > > > [email protected]> wrote: > > > > > >> The Riemann–Darboux approach seems so much easier. Just take a range > > and > > >> a step interval (resolution) (all as y) to iterate the function > (adverb > > >> argument) and add all the results up divided by number of intervals > > times > > >> range. > > >> > > >> > > >> > > >> > > >> > > >> > > >> On Thursday, January 14, 2021, 04:21:19 p.m. EST, Devon McCormick < > > >> [email protected]> wrote: > > >> > > >> > > >> > > >> > > >> > > >> Has anyone looked into implementing a Lebesgue integration adverb in > J? > > >> This looks like a good explanation of it: > > >> https://en.m.wikipedia.org/wiki/Lebesgue_integration . > > >> > > >> -- > > >> > > >> Devon McCormick, CFA > > >> > > >> Quantitative Consultant > > >> ---------------------------------------------------------------------- > > >> For information about J forums see > http://www.jsoftware.com/forums.htm > > >> ---------------------------------------------------------------------- > > >> For information about J forums see > http://www.jsoftware.com/forums.htm > > >> > > > > > > > > > -- > > This email has been checked for viruses by AVG. > > https://www.avg.com > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > -- > > Devon McCormick, CFA > > Quantitative Consultant > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
