Do we have a way to define Taylor polynomials for functions of several
variables with respect to just one variable? Specifically, I'm
thinking about Taylor polynomials Bessel functions with a fixed
order. We have:
(%i1) taylor(bessel_j(1/3,x),x,0,5);
taylor: encountered an unfamiliar singularity in: bessel_j(1/3,x)
A better answer is something like (a polynomial in x^(1/3))
number * x^(1/3) / gamma(1/3) + number * x^(2/3) / gamma(1/3) + ...
Worse, taylor(bessel_j(1/3,x^3),x,0,5) gives the same error.
Looking at hayat.lisp, I see the known-ps mechanism for extending
taylor, but it seems that this doesn't work for functions of several
variables (but it does work for subscripted functions (for example
psi)).
We do have deftaylor, but again, this mechanism only works for
one-variable functions.
--Barton