求下列周期函数的傅里叶级数展开式:[tex=5.571x1.286]poXx9kzw7gxFgsEa9Qp7sEY4aEblMoGWnnSty8zDy2w=[/tex]( 周期 [tex=0.643x1.286]USGVpa36zb6HMu8k0moHJA==[/tex])
解: 首先在 [tex=2.929x1.286]oOkR6vfxpqR/nMbArHbdwbn0ohLswcPDhoZF037gnvg=[/tex] 上将函数 [tex=5.571x1.286]poXx9kzw7gxFgsEa9Qp7sEY4aEblMoGWnnSty8zDy2w=[/tex] 展开成傅里叶级数由于 [tex=14.429x8.214]SMCiZCjCLMG8LLJWa9iOzFGreRUFsM2fhNoSV14jSgfd7aecfY9rRupvodPKCeSSswREwUkUaPnYGTXwqlAOf2G0K7/QRGAE9F83x2/VAl10Jc+UVU8criwmnp2YrpjxgyPDfTUkKDj/gAcX3BAFkkAw7dDVq27yEuoDqo5hHstRr5p3+4Sz2tC4g6fJ8adP9x2dgoTyRST70hZAYKNJ26mjwTWNsdQDJT6Mchw2qJGr1LON3D4378NGZY9tlxgzeUrP2cXqEvmi3t4FcPF8sSqhKi69TjRQgXFc4v0uO0c=[/tex]故有[tex=19.214x5.786]qeiYnKXLEhyhuGRg8yLtr2S+yy7xPzyVaT06R6e3DPfS7NsXkWOENhDlRJGhMo+zt0bfr4eOFqRIhG0eJbSBO+RNgC7eu67ai0r9uTXwJGqwYsZKwD/3wwm8gOndjHpzcazJ7ItlF8h6EGG3bvYmpGJkOP/lWE0gDvHNgsVN2cdmFn8jDzDXITuhKWl5KcKm+AbXRY6JHlzqxXhL+iq9IeHtSZQ3hM3oFsH+8bPsepB//fCj1dFugn+1fV0pXeIa94qDmMeIgBvo+zXGxmWuS3hfvEzURTXxEw4oYuwQVKs=[/tex][tex=20.929x3.071]qeiYnKXLEhyhuGRg8yLtr75zXc1bK9GK+XI6HE83NDfs9vM6ds+miKdnrREtTV2rYvOhtxo+9r3e8Vz9zwa3Xqsexnnbzzx6R+S2gYNLvsMD/djlbXOavSGyQEtm1VXJh5rRnZcfDIlLjYKho5sMLeVPb0iGhOuFHjxj3rcozClRDk3ufsSh2nSoBDhggb2oeC7JIzlqT/Z3j+WU/sTTaA==[/tex][tex=7.143x5.929]Pz6X3gZVGc44O8UoFyALGHfe2BcSyzD3v1L9DmmXCiVvzlQD/4O958xIA3gZOyav7xW7j38Uig+M2lgyougeioLyrkkibfBGd0Upr06qWdnbvtS40ICWQhCRVbYhvM94[/tex][tex=12.071x2.714]8sS7wcqU+wrMNXAXCGnru7xmcaq1njRlrxPLPeeAG6aNUAn547MfqmaAvKhkM9G/ccil2lJKqL8s2+LzEYEOMwBWtFJzM/zgx9WRML/PQYY=[/tex], [tex=4.857x1.286]YPiXln35VbFZwRw1qebPNC/mxvz5Wi8NCIeJXzYWeYc=[/tex]因为函数 [tex=1.857x1.286]G6WxJ307HB2e1l7Qz3uNbQ==[/tex] 光滑, 根据收敛定理[tex=12.571x2.357]ZRYTiGk9bXzdxJ3CqI+7ONpPWzMwVzqJFZZ38/Jw8mNCcVEBRqRd0RPSaYTWcHRkdx1LJHFLcKCScTDImDFMHDlUPO24cwZTRGJHW/8m52M=[/tex] [tex=7.286x1.286]TON6UGaHEK8MOj43EJUxxt6bBbjuxSYs4bqAhxg6Wso=[/tex]
举一反三
- 求下列周期函数的傅里叶级数展开式:[tex=5.857x1.286]qMOLsARs2Ww+rZ87Gf3UqkRFv4VMGpbOjRzRZ3JBlsY=[/tex] (周期 [tex=0.643x1.286]USGVpa36zb6HMu8k0moHJA==[/tex]) .
- 求下列周期函数的傅里叶级数展开式:[tex=6.0x1.286]bQVUWNAQtxnnx3MDKSPt5Q==[/tex] (周期1).
- 求下列周期函数的傅里叶级数展开式：[tex=7.143x1.357]qAU07a/UMA9qmDdYIFZHiuDbQciYplFbD010frnC35s=[/tex]（周期[tex=1.071x1.0]cWYnFY7tUlCT6WhMhv7goA==[/tex]）
- 将函数[tex=5.571x1.286]poXx9kzw7gxFgsEa9Qp7sEY4aEblMoGWnnSty8zDy2w=[/tex]展开成傅里叶级数．
- 求下列函数的傅里叶级数展开式：[tex=8.214x1.357]kEPI5WwnwC/4osrhuwcJn1bEYDNSfFo9tjF3JhtLWkk=[/tex]
内容
- 0
求下列函数的傅里叶级数展开式：[tex=10.143x1.357]qAU07a/UMA9qmDdYIFZHilEJmiBRkoK3A8RHEzZ4P4W8f1Zgl8fZyxMJ2QQ6azCB[/tex]
- 1
求下列函数的傅里叶级数展开式：[tex=10.429x2.286]i41q0BRTWZJQmNRPJQhH+gumwgQDzGqtl/61T6v1cRw=[/tex]
- 2
求函数系的傅里叶级数展开式:[tex=7.786x1.286]lKoao7AHJRlCMQaCikocwd9FkYgBIUtHum5SptVMYS0=[/tex],[tex=5.071x1.286]Y9nIBZA1Le7w9q8FIC0XtoPFAMFg+TzqgyUq4oFDpNDYqB7143ZGAm8mHpbxFBSP[/tex].
- 3
求下列函数的傅里叶级数展开式：[tex=10.071x1.357]5cM/LvJqoCikO7A5c+WCIFvkMrcH8wM/sSdNFcbb5l7CiIY7PXE8owHe7h0e7UQ9[/tex]
- 4
求函数系的傅里叶级数展开式:[tex=4.786x1.286]nH2DJmYYQnPd2rudvdBaoAdZmPf1q4U8JS4et/PM1E4=[/tex], [tex=5.071x1.286]dJuo9ok621YT5T6DdN5n6Q==[/tex].