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l := Pi ;  c = 1 ; alfa = 0 ; beta = 1/4 Sin[2 x]

1/4 Sin[2 x]

A[n_] := 0 ; B[n_] := 2/(c n π) ∫_0^lbeta * Sin [(n π x)/l] x ; ;

Table[{A[n], B[n]}, {n, 10}]

{{0, 0}, {0, 1/8}, {0, 0}, {0, 0}, {0, 0}, {0, 0}, {0, 0}, {0, 0}, {0, 0}, {0, 0}}

u[n_, x_, t_] := (A[n] Cos[(n π c )/l t] + B[n] Sin [(n π c )/l t]) * Sin [(n π)/l x]

u[2, x, t]

1/8 Sin[2 t] Sin[2 x]

u[x_, t_] := Underoverscript[∑, n = 1, arg3] u[n, x, t]

u[x, t]

1/8 Sin[2 t] Sin[2 x]

Created by Mathematica  (December 3, 2003)