# Wrong Result in Computing the Laplacian

I am using Mathematica 11.0.1.0. I have the following simple code

ClearAll["Global*"]

L[f_] := Laplacian[f, {r, \[Theta], z}, "Cylindrical"]

B[f_] := Laplacian[
Laplacian[f, {r, \[Theta], z}, "Cylindrical"], {r, \[Theta], z},
"Cylindrical"]

f = Subscript[A, 1] z^3 +
Inactive[Sum][(Subscript[P, i] Sinh[Subscript[\[Alpha], i] z] +
Subscript[Q, i] z Cosh[Subscript[\[Alpha], i] z]) BesselJ[0,
Subscript[\[Alpha], i] r], {i, 1, n}]

L[f]

(* 6 z Subscript[A, 1] *)

B[f]

(* 0 *)


The result that Mathematica is giving for the Laplacian is wrong. The true answer is

$$6A_1z + \sum_{i=1}^{n}2 Q_i \alpha_i \sinh(\alpha_iz) J_0(\alpha_i r)$$

However, when I remove the sum the true result can be obtained

f = Subscript[A, 1] z^3 + (Subscript[P, i] Sinh[Subscript[\[Alpha], i] z] +
Subscript[Q, i] z Cosh[Subscript[\[Alpha], i] z]) BesselJ[0,
Subscript[\[Alpha], i] r]

L[f] // FunctionExpand

(* 6 z Subscript[A, 1] +
2 BesselJ[0, r Subscript[\[Alpha], i]] Sinh[
z Subscript[\[Alpha], i]] Subscript[Q, i] Subscript[\[Alpha], i] *)

B[f] // FunctionExpand

(* 0 *)
`

Can anyone help me with this and say what is going on here?

• Can't reproduce your results in 11.1. However, it spits out some complicated outputs along with some error messages. I'm able to get the correct answers (not fully simplified) by replacing Inactive[Sum] with Sum. – W.Mason Mar 27 '17 at 12:29
• I would suggest not using Sum at all. – W.Mason Mar 27 '17 at 13:01
• @W.Mason: I am using 11.0 so I should do some updates maybe! :) – Hosein Rahnama Mar 27 '17 at 13:08
• @W.Mason: See the updated question. I figured it out that how to obtain the correct result. It seems to be a bug in Mathematica 11! – Hosein Rahnama Mar 27 '17 at 13:52
• Well, of course it works when you remove the Sum. It could be a bug with Inactive[Sum] in Mathematica, but Sum alone in 11.1 works OK (hard to simplify the answer unless I remove Sum). I think Sum should altogether be avoided in such calculations, at least until these problems are fixed. – W.Mason Mar 27 '17 at 14:22

## 1 Answer

This is a bug, plain and simple. If you use Sum instead of Inactive[Sum], it works in both 11.0 and 11.1.

I'm pretty sure I know what was the bug in 11.0 and that I fixed that particular bug in 11.1. Unfortunately, there now seems to be a bad interaction with our new indexed-differentiation code which is producing a different wrong answer in 11.1. I will investigate and try to fix this for 11.2. If I come up with any more general workarounds, I will post them here.

• (+1) Thanks for the attention. :) I reported this bug. :) – Hosein Rahnama Apr 3 '17 at 19:54