Waldek Hebisch <[EMAIL PROTECTED]> writes: > > But the behaviour is consistent for Gamma, Bessel and Polygamma. It is not > > difficult to change this behaviour to leaving the derivative unevaluated, > > but I'm not sure whether that would really be better. If you are > > absolutely sure, please let me know as soon as possible. > > Yes, currently we produce mathematically incorrect result. In principle user > may get wrong results even if input does not contain explicit derivative.
Oh? How is that? > Once we get better support for special functions this may be very serious > problem. Probably. By the way: most (probably all) special functions would be covered by my favourite would-be category/domain hierarchy of differentially algebraic functions. Then we could say something like polygamma(a, x)$HOLO(???) and get the corresponding differential equation. > I supect that original author did not know how to leave one partial > derivative unevaluated, while giving value of the second one (ATM this is not > clear for me either). If you know how to to this please go on. OK, I will. > > How about polygamma? should D(polygamma(x, x), x) throw an error? I guess > > so. > > But if we follow you, Bessel* should leave the derivative with respect to > > the > > first argument - i.e., leave it unevaluated. > polygamma(a, x) has sensible definition also for non-integral a, so just > leaving D(polygamma(x, x), x) unevaluated is reasonable. I could not find such a definition. Could you please send me such a definition or a reference? > Since in other places we support only integral a error is reasonable too. > For Bessel* leaving derivative with respect to the first argument unevaluated > is preffered to error -- we can still do some calculations with unevaluated > derivatives. Yes. Martin _______________________________________________ Axiom-developer mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-developer
