@Markiyan Hirnyk Just plain integrate it:

int(BesselJ(2, r*k)*BesselJ(1, 1500*k), k= 0..infinity);

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@Markiyan Hirnyk Thanks. I got all files from Christopher's attached zip file.

Please supply (as an attached worksheet) the complete code that you used to read in the data. And please also attach the data files.

The worksheet that you display in your Question is not exactly the same as the one attached to the Question. For example, the displayed one defines a function TS1, but in the attached it is TS[1]. Please attach the most recent copy of the worksheet.

@Thomas Richard 

There are two problems with using interface(displayprecision), one big and one small. The small problem is that every float is shown to that number of decimal places even if that means adding extra zeros. That's just ugly. Example:

A:= < < .1, .2 > | <.3 , .4> >;

The big problem is that it actually changes the number of decimal places to which a result is shown, not its precision. Example:

A^18;

So there is really only one digit of precision in second column, and zero digits of precision in the first column.

@Markiyan Hirnyk I said that some OTHER operations (not Matrix operations) were done so that the final result is accurate to Digits precision. This is standard English usage of the word "other".

@Markiyan Hirnyk 

Yes, the roundoff error is greater. By setting UseHardwareFloats:= false, the computations are done internally at 5 digits precision also. This is different from a lot of other floating point operations where the number of digits is increased internally so that the final result is accurate to Digits precision.

I deleted your copy of this question from yesterday. Please edit a question instead of making a new copy. Editing a Question will place it back at the top of the Active Conversation lists, so there's no benefit to making a new copy; you'll only annoy people by doing it.

I am sorry that there's not many people on this forum who know MapleSim, including me.

@mehdi jafari

You can construct the sequence with n unknown by using $ instead of seq:

S:= P(j,n) $ j= 1..n-1;

Then specify n later:

n:= 4:
S;

Could you provide a more-detailed example please? Show me precisely an example of an "arbitrary function" and what you consider to be its dependent variable(s). Show me precisely an example of the type of input expr you want your procedure to take. And what do you mean by "matching" the "dependent variables list". How can there be more than one dependent variable?

Look at ?Statistics,NonlinearFit . Note that the independent variables are passed in as a list, the parameter v. The value of the expression falg is implicitly the dependent variable, so there is no dependent variable that appears explicitly in the input.

I think that you may be confusing dependent and independent variables.

@Bruno Gobin You are using a very crude workaround so that you can use sum in a way that it was not intended to be used! The problem is solved by using add instead of sum. Quoting from ?sum :

To add a finite sequence of values, rather than compute a formula, use the add command....  Although the sum command can often be used to compute explicit sums, it is strongly recommended that the add command be used in programs if an explicit sum is needed....

@J4James 

You may get better results by animating (2D) contourplot instead. Then you'll get 65 contours in every frame because it won't be constrained by the z-axis. But... The contours will not represent the same level curves in different frames.

@delta7 Ah, that works also.

To see all the color names (there are hundreds) issue the command:

ColorTools:-GetColorNames(),
seq(ColorTools:-GetPalette(P), P in ColorTools:-PaletteNames());

@J4James You must use the same view option in both the animation and all the static plots.

@J4James

In the static plot, include the option view= [DEFAULT, DEFAULT, -35..1]. Then it will look exactly like the last frame of the animation.