How to define many arguments in function?

Question

Following is my code, you can see that in eq[], its arguments are defined by t and list{xs}, If I expand the list{xs}, I have to write a lot of λ. Could you help me to simplify the definition of eq[]? When I wanna set λ from λ1 to λ1000, how can I achieve that?

Clear[n, λs, xs, tvalues]
n = 5;
λs = Symbol["λ" <> ToString[#]] & /@ Range[n](*number of sites*);
xs = Append[λs, β];
tvalues = Range[0., 1., 0.01] (*set of t values*);
randnum = RandomReal[1, {10, n + 1}];

Clear[eq]
eq[t_, {λ1_, λ2_, λ3_, λ4_, λ5_, β_}] = 
  Block[{U = 1., μ = 0.5, ϵ = (-2 t - 0.5), EE, summand},

   EE[k_] := (-2  t ( Cos[(2 π  (k - 1))/n])) - μ;
   summand[λ_, k_] := (U/(2 n)) (Cosh[λ]^2 Sinh[λ]^2 + 
        2 Sinh[λ]^4 + 
        2 β^2 Cosh[λ] Sinh[λ] + 
        4 β^2 Sinh[λ]^2 ) + Sinh[λ]^2 EE[k];
   Total[MapIndexed[summand[#, #2[[1]]] &, λs]] + ( β^2 ϵ) + (U/(2 n)) (β^4)
 ];

```

Answer 1

Define your function using the following (note also the :=):

eq[t_, {lambdas__, β_}] := (* rest of your code *)

then inside the code change λs in MapIndexed[summand[#, #2[[1]]] &, λs]] to

MapIndexed[summand[#, #2[[1]]]&, List[lambdas]]]