⑩天掌 Teaching Plan on Advanced Mathematics o =1(2k-1)2z ,n=2k-1,k=1,2, n=2k,k=1,2 f∫(x) sinned (rsin ndt 一飞 sinned=0,(m=1,2,3,…) 所求函数的傅氏展开式为 2=(2n-1) c0(2n-1)x(-兀≤x≤π) tianjin polytechnic dmivendityTianjin Polytechnic University Teaching Plan on Advanced Mathematics     = = = − = − − =   0, 2 , 1,2, , 2 1, 1,2, (2 1) 4 2 n k k n k k k     − bn = f (x)sinnxdx 1    −  − +  = 0 0 sin 1 ( )sin 1 x nxdx x nxdx= 0,   = −  − −  = 1 2 cos(2 1) (2 1) 4 1 2 ( ) n n x n f x (−  x  ) 所求函数的傅氏展开式为 (n = 1,2,3, )