@HS That depends on whether x is the special field element (defined with alias and RootOf) or just a variable.

Your syntax problem is extra multiplication signs, plainly visible in the plaintext code in your Question. These probably come from extra spaces in 2D Input. In 2D Input a function name (such as Expand) must be immediately (without intervening spaces) to the left of the left parenthesis that begins its arguments. In 1D input, it doesn't matter. 

And do you want to do it in Maple Companion? 

Someone with the power to do so needs to add Maple Maple Companion to the Products list for Questions here.

@Rouben Rostamian  Yes, NextZero can be somewhat unreliable in that regard for functions that have an extreme number of vertical asymptotes, as this one does.

However, my Answer did show 245.3396184 and 481.5561050; you just need to scroll to right. Regarding 530.0902992 and 578.7535346: I'll admit that it looks like the function has roots near those values, but putting those numbers into the function at Digits=15 returns values far from 0.

@Joe Riel Neat trick. I'd only ever considered that for alternate spellings. It should be noted that the way that the unevaluation quotes work in _options['view'] is very special. Using 'view' or 'zoom' elsewhere in the procedure, the quotes have no effect, just like any procedure parameter. However, ':-view' and ':-zoom' act normally.

@mehran rajabi You can get some more roots like this:

Digits:= 15:
R:= table():
r:= 49.32883964:
Eq:= unapply(eq, x):
while r::numeric do 
    r:= RootFinding:-NextZero(Eq, r, maxdistance= 1e9);
    R[r]:= NULL
od:
indices(R, nolist, indexorder);
68.9303311172937, 106.974056704266, 151.062435474302, 198.382622867143, 245.339618384328,
291.310838331266, 338.964900033057, 387.685839558259, 434.873481747309, 481.556104974205,
672.896169599596, 721.880328695120, FAIL

The fact that FAIL was the last value returned doesn't necessarily mean that there are no more roots; it just means that NextZero gave up. If you want to search for more roots, let me know.

The following plot has 3 curves: red, blue, and green. The red one is your original linear interpolation. The green (vertical) corresponds to x = 808. The blue is another linear interpolation using the L[1] values in place of x[12]. Please explain the connection between this plot and what you actually want.

restart:
V[Ed13]:= <257.184, 230.4, 184.3, 138.2, 92.2, 46.1, 0>:
x[12]:= <-149, 208, 567, 925, 1283, 1642, 2000>:
L[1]:= <0, 358, 717, 1075, 1433, 1792, 2150>:
plot(
    [<x[12] | V[Ed13]>, < L[1] | V[Ed13] >, [[808,0], [808,250]]], 
    thickness= 2
);

@mmcdara Okay, it works in Maple 2019, but it's clunky unless you stabilize the extent of the vertical axis. That is, it helps if the vertical axis has the same "mathematical" length across the whole parameter range. You can do that by including a view option, or simply change the plot command to

plot(f, x= -3..3, 0..0.5)

Your worksheet is missing a definition of f. I assume that that just got deleted accidentally somehow, because it makes no sense (at least to me) without that definition.

We need to look at more-specific cases. Certainly it works in some cases, such as

asympt(HeunC(a, a, b, b, c, 1/z), z);

(works in Maple 2019).

@imparter 

Your first error above is that IBC is still not a set! It should be {IBC}.

The second error above is that you have Pa=0 where you should have Pa:= 0.

After you correct that, it'll complain that you don't have enough initial conditions. It wants 5. The only thing in your IBC that it considers an initial condition is p(r,-1) = 0.

The other post of mine that you linked to is not yet relevant! Your input hasn't even been accepted by pdsolve yet. Forget about the plots until the pdsolve is fixed,

Do not post followups as separate Questions!

You should start by entering the 5 equations, 5 solutions, and the intermediate variable definitions into Maple. Then, it should be very easy to verify that it is a solution. It may be a little more difficult to verify that it's the only solution.

You should change I and D to different variables because those are otherwise used by Maple.

@Kitonum The OP is referring to the kind of plot produced by Statistics:-ColumnGraph.

@Kitonum Based on the picture in the first version of this Question, I know that the intention is that k is a fixed number between 0 and n, inclusive.

@daljit97 I see that you've attempted to correct the Question. But "multiplication modulo 42" is not the same thing as "modular multiplication by 42". The former is the correct group operation. The latter isn't even a binary operation, let alone a group operation.