Applying a function f to a square matrix A is done by performing an eigenvalue decomposition A = PDP^(-1) (where D is the diagonal matrix of eigenvalue) and then setting f(A):= P.f~(D).P^(-1). If there were two matrices, there would be no well-defined way to pair the eigenvalues.

If you could compute a multivariate Taylor series for BesselY(x,y), then the matrices could be put into a trucated series for numeric approximation. But I don't know how to compute that series.

@tomleslie 

The only syntax error that I found was the lack of quotes on union. What were the "several"?

@gkokovidis 

For one thing, I see no evidence in the original Question of missing multiplication signs or their equivalent in 2-D input. For another thing, I entered the integral in 1-D input (with explicit multiplication signs, of course), and my computer crashed utterly and completely after several minutes. There was no loss-of-kernel message and no access to Ctrl-Alt-Del---I had to turn it off with the power switch. This is Maple 18.2-64 under Window 8.1.

@Kitonum 

The distinction is not between Ctrl+l (lowercase L) and Ctrl+L but rather between Ctrl+L (which works) and Ctrl+Shift+L (which doesn't work). For example, if Caps Lock in on, then Ctrl+L still works and Ctrl+Shift+L still doesn't work. This same distinction could be made for any Ctrl+letter combination, and it is long-standing tradition, not just in Maple, that the letter be capitalized when referring to any such combination.

The above applies to Windows. I'm not sure about the other OS's. But the part about the long-standing notational tradition is much older than Windows. It goes back at least as far as 1978, which is when I started using computers.

@Markiyan Hirnyk 

Glad to know it. Joe's one of the best writers on here. I hope to see more of his work soon. I added an attribution.

@Christopher2222  FWIW, I do remember the post and animation.

@farzane 

I can't provide any more help unless you can address the issue that I raised. Specifically, in order to get a 2D plot, I need to eliminate another variable. The primary way to do that would be to have one more equation.

Also, what do you mean by the "rate" of x? Do you mean a derivative?

@tomleslie The OP is asking whether the fonts, colors, orientation, lighting, transparency, etc. can be or should be changed in order to publish the plot on paper.

To the OP: You should read the help pages ?plot,options and ?plot3d,options to get an idea of the options that are available for plots.

@PunkRediska 

A list of lists of constants can't be a variable. Are you trying find the minimum value of a function over a finite set of pregenerated points? You don't need any fancy minimization software for that. Just evaluate the function at all the points and use min.

@ecterrab 

Yes, I believe that you are missing something. Zero isn't a positive integer. The examples that you've shown where you put a lower bound of 1 on the sum j+k have indeed restricted that sum to be greater than 0, but they don't restrict the individual variables. I want both j and k individually restricted to positive integers. (And, as I said, I don't think that that's an unusual request.)

Here are two examples. The first example shows both j and k taking the value 0. The second example is weirder. It shows j restricted to positives, but k allowed to be 0. I don't know how it has made a distinction between j and k.

(The worksheet uploader is broken right now. I'll just post the input and plaintext output by cut-and-paste.)

restart:
Physics:-Setup(redefinesum= true):
Sum(f(j,k), ''1 <= j+k and j+k <= 2'');

value(%);

     f(0, 1)+f(1, 0)+f(0, 2)+f(1, 1)+f(2, 0)

Sum(f(j,k), ''1 <= j+k and j+k = 2'');

value(%);

     f(1, 1)+f(2, 0)

@ecterrab 

You misunderstood my question; sorry that it wasn't more clear. Yes, I've tried the command and read the help page. So I know that it works when you change the initial value of m. That is obvious. I want to change the lower limit values of j and k. For example (and this seems like a fairly common situation), I want the inner sum to be done for all pairs of positive integers (j,k) such that j+k = m-1. 

Unrelated question: When you programmed this, were you able to prettyprint the sum with an inequality on the bottom using just Maple-level programming, or did it require a change in the GUI?

@ecterrab In this new form of Sum command, with index expression j+k= m-1, how does it know the initial value of j? In this case it was obvious that j needed to start at 0, but if m started at 3, say, then there could be a case where the intended start for j is 1.

It looks like you're trying to supply more than one initialpoint to Optimization:-Minimize. It doesn't allow that. You may be better off using the DirectSearch optimization package (which you'd need to download from the Maple Applications Center). That package's commands allow for multiple initial points.

You can rerun Optimization:-Minimize pm times, once for each initialpoint.

There are some things confusing about your Question:

1. The Minimize doesn't use getone; indeed, you don't give any purpose at all for getone.
   
2. You use z several different ways. You have it as the objective function, the sequence of variables of the objective function, a randomly generated point, a list of randomly generated points.

You can simplify your random point generation like this:

Roll:= rand~([98.0..102., -1.0..5., .5..1.0, 0..evalf(2*Pi), 0..20.]):
['Roll()'$pm];

Do you want differentiation with respect to a particular variable, such as x, as provided by the diff command, or differentiation of an operator, as provided by the D command?

@maple fan There's no real root! If there were a real root, how would you decide if it was positive or negative? Maybe you just want to make it negative? Okay, then plot

plot(-abs((-2)^x), x= -sqrt(2)..-exp(-1));

So what's the real root of (-2)^(1/2)?