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三、常用信号的拉普拉斯变换 常用信号的拉普拉斯变换4. t 的正幂函数 t n,n为正整数t n st ∞ n ∞ n 1 st L[t n u (t )] = ∫ (t n )e st dt = (e ) 0 + ∫0 t e dt s s n ∞ n = ∫0 t n 1e st dt = L[t n 1u (t )] s s 根据以上推理,可得∞ 0
n n n 1 n 2 n 1 L[t u (t )] = L[t u (t )] = L[t u (t )] s s s n n 1 n 2 2 1 0 = L L[t u (t )] s s s s sn
t u (t ) ← →n L
n! , Re( s ) > 0 n +1 s