# Defining functions with changing number of variables [duplicate]

I am working with a bunch of functions of the form

fn[x1_,x2_,x3_,...,xn_] := x1x2+x2x3+...+xnx1


where $n$ changes. Is there a way to create these functions efficiently, without having to explicitly define each? I'm looking for a way of declaring, say, $n=5$ and getting back

f5[x1_,x2_,x3_,x4_,x5_]:=x1x2+x2x3+x3x4+x4x5+x5x1


Perhaps they could be defining iteratively? Since fn and fn-1 only differ by a few monomials. I appreciate any helpo that I can get! Thanks!

edited to include comment from Kuba

From the manual: "BlankSequence is a pattern object that can stand for any sequence of one or more Mathematica expressions."

f[x__] := (Print["The number of parameters passed is: ", Length[{x}]]; {x}.RotateLeft[{x}])
f[a1, a2, a3]
(*The number of parameters passed is: 3*)
(*a1 a2 + a2 a3*)


Note that you must give a head to that sequence of parameters. In the example above, the calculation of the length of the parameters is not just Length[x] but Length[{x}]. The function you requested is:

f[x__] := {x}.RotateLeft[{x}]

• You are right, I'll edit the answser. – Hector Aug 16 '13 at 16:19