The equation should be:
u ( x , y , t ) = ∑ n = 1 ∞ ∑ m = 1 ∞ sin ( n π x L x ) sin ( m π y L y ) ( a n , m sin ( ω n , m t ) + b n , m cos ( ω n , m t ) ) {\displaystyle u(x,y,t)=\sum _{n=1}^{\infty }\sum _{m=1}^{\infty }\sin \left({\frac {n\pi x}{L_{x}}}\right)\sin \left({\frac {m\pi y}{L_{y}}}\right)\left(a_{n,m}\sin \left(\omega _{n,m}t\right)+b_{n,m}\cos \left(\omega _{n,m}t\right)\right)}
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