Surface fitting involving factorial function [closed]

I have a large data set made up of triples, (x, y, f(x,y)), x, y and f(x,y) are all integers. I don't know the function f(x, y) and my goal is to find (estimate) it. I do know that x can be any positive integer and y varies from 2 to x. We have a feeling that f(x,y) involves x!. This seems to be a surface fitting problem. However, it seems that MATLAB doesn't have a way to do surface fitting for a factorial function. Does Mathematica, SAS or any other software have this capability? Any help in this regard will be highly appreciated.

closed as off-topic by MarcoB, user9660, Kuba♦, Yves Klett, Michael E2Jun 28 '16 at 16:32

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• As the lot of us neither have your data nor any capability to read your mind, it will be difficult to help you unless you can resolve one of those two concerns. – J. M. is away Jun 27 '16 at 10:32
• How about something like FindFormula[data, {x,y}, TargetFunctions -> {Gamma[x]}?, Perhaps there's a way to specify Integers? – Feyre Jun 27 '16 at 11:30

1 Answer

I am going to give an answer from my hunch. Say your function is 0.3 y + 2/x!. To fit this function you can use Gamma[x] instead of x!. The result would not be very good as the interpolation will go over non integer values as well.

data = Flatten[Table[{x, y, .3 y + 2/x!}, {x, 0, 10}, {y, 0, 10}], 1];

f = a /Gamma[x] + b y
FindFit[data, f, {a, b}, {x, y}]


{a -> 1.23441, b -> 0.327027}

For a better answer, we need better information. After all, as J.M. pointed out, we can't read your mind :)

• OP states "x, y and f(x,y) are all integers" so the choice of function is perhaps a bit poor. But the method you show is of course the point, and a good one :) – Marius Ladegård Meyer Jun 27 '16 at 11:11
• Adjust your model since x! == Gamma[x+1] and the fit will be very good. Or just use x! since it is defined for more than just integers. – Bob Hanlon Jun 27 '16 at 13:45