I tried to expand BesselJ[k,x]
function into a Taylor series with Series
command. Here both k
and x
are some functions of the expansion variable $\lambda$, so in the expansion, derivatives with respect to both k
and x
occur.
The problem is, whenever there is a term that is the derivative of both variables, Mathematica leaves it as (e.g.) Derivative[2, 1][BesselJ][0., 2.40483]
and doesn't give a numerical value in the end.
First I thought it is because assigned values aren't exact -- since the above 2.40483
is the value of BesselJZero[0, 1]
. However, it also doesn't give numerical or analytical result for the following easier calculation:
D[BesselJ[k, x], {k, 1}, {x, 1}] /. {k -> 1, x -> 1} // N
(* -> Derivative[1, 1][BesselJ][1., 1.] *)
But, when the order of the differentiation changes, it gives numerical results:
D[BesselJ[k, x], {x, 1}, {k, 1}] /. {k -> 0, x -> 1} // N
(* -> 1.22713 *)
It works with x -> BesselJZero[0, 1]
as well.
First question: why is this the case?
Second (if it is possible): how can I handle it with Series
command?
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) as an apostrophe ('
)! $\endgroup$