@Axel Vogt 

Every rank 1 matrix can be generated as x.y^%T for nonzero vectors x and y. Since there are 15 nonzero 4-vectors over Z[2], there are at most 15^2 = 225 rank 1 matrices. That still doesn't answer for me why Kitonum's code works, but his 225 seems plausible.

@GPY 

Yes, and make alpha a parameter to dsolve. And I hope that you'd only be doing that for fixed values of v0.

@Axel Vogt What's the point? The answer is unique, so interpolation gives the same thing.

@Saeed I don't see any inaccuracy in getting the points from the graph. After all, how is the curve represented in the computer? It is an ordered collection of (x,y) pairs.

@Saeed Get points from the graph. If the graph exists in any computerized form, that should be fairly easy.

@Carl Love My Answer above has been significantly updated.

Nobody wants to retype your integrals. So please post your work as a worksheet. You can use the green uparrow, which is the last item on the second row of the toolbar in the MaplePrimes editor.

@Chris_45 

I have tried Statistics:-NonlinearFit on many different interpolating models, including sines, exponentials, rational functions, and products and compositions of these. I can't get any reasonable fit. The "associated function" for my ArrayInterpolation curve is a piecewise cubic spline with very many pieces. I doubt that that would be of much use to you, but if you want it, just use Preben's Spline command.

Part of the problem is that your independent variable, y_data, is very unevenly spaced: It has huge gaps in the middle and is very tightly spaced at the high end.

This is just an aside, not an answer to your Question. If you know that your sums can't be evaluated, you should use Sum instead of sum. If you use the latter, the system wastes time trying to evaluate and re-evaluate the sums everytime the expression containing them is used. Also, one of your transformations may lead to an unintended simplification.

@brian bovril 

Could you provide a more-standard reference to the paper so that I can find it?

@Carl Love 

I don't know much about Maplels, but I found the following in the help page ?Maplets,Elements,TextField: The command Maplets:-Elements:-TextField has an option tooltip= "...".

@Alejandro Jakubi Thanks for spotting. Code corrected above.

@JohnS Pattern matching "any name except x" is possible like this:

define(
     L, orderless, multilinear,
     L(a::And(name,Not(identical(x)))*b::function, c::function) = a*L(b,c),
     L(
          a::And(name,Not(identical(x)))*b::function,
          c::And(name,Not(identical(x)))*d::function
     ) = a*c*L(b,d)
);

@JohnS Under your definitions for L, we have L(x*f(x)) = x*L(f(x)). If that makes sense for your application, fine; but it doesn't fit my usual conception of linearity.

@JohnS 

It will work if you first put them on the sequence of constants:

constants:= constants, c, d, e, f;