f(a,b) = f(a +b)

[Bruce Boghosian]

   Date: Wed, 7 Aug 91 09:22:30 -0400
   From: Charles Bachmann <bachmann at radar.nrl.navy.mil>

   In reply to Steve Ingrassia's comment , what about f(x,y) = 1 /(x + y).
   We can think of it as a function of two variables, but with the replacement
   of z = x + y, it becomes a function of one variable f(z) = 1 / z.

At the risk of splitting hairs here, most mathematicians would probably
like to see a different symbol used for the second function.

So, the question is (presumably) to characterize functions of two
variables, f(x,y), that have the property that there exists a function
of one variable, g(z), such that f(x,y)=g(x+y).

I know of no particular name for such functions.  They satisfy the PDE

partial f   partial f
--------- - --------- = 0,
partial x   partial y

but that's probably not a particularly useful characterization either.

--Bruce