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  • 2022-06-15
    下列函数是以 [tex=1.071x1.0]tieuzjBYrMcmxP3HXZSPGQ==[/tex] 为周期的周期函数， 它们在 [tex=3.071x1.357]UGbKMXer1fUi6HhYH2aB/A==[/tex] 上的表达式如下，试将它们展开成傅里叶级数: [tex=10.286x1.5]youph0rT5CBew5Tr5fay/SfykIXLEy0oR4QRTlTkyVESc9zokCnBtMuFqanO6RI5[/tex]
    • 解：所给函数满足收敛定理的条件，它在点 [tex=13.071x1.357]C+DtjiyC8JX5+BP7OMjwFAnSUuGO64djcm99WyF1zj7lpAUk+jnBzOLLNocn7MUT[/tex] 处不连续，在其它点处均连续，从而由收敛定理知道 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 的傅里叶级数收敛，当 [tex=5.143x1.357]bETSghj0+ch1t8l5iNjhYw==[/tex] 时级数收敛于 [tex=4.571x2.5]wTyCFqnur8gRsSB548fS+BUMcdgCmQ/Etj0yn2DIbHDXjLuwbPl74s9dnt3arb5m[/tex] 当 [tex=5.643x1.357]yNPtdrFYcHk4QdA+STKSdhQkXO1utN9D2oPEU6Ls6No=[/tex] 时级数收敛于 [tex=2.143x1.357]BazjA76tgLiCVqPsTb0axw==[/tex][tex=25.643x2.857]tHLdoaX6J1rkviYwGYKM9V6ySpnnY62XXNAu5Chj/cu/fsoXhYbB95QPITYBNkH8NI9R/d9aHb7lugPAcZlcUqWNYXg8HdQUpVERNVwxLEJHTsFBZpj+KFtHrnS6JEzB0VPIDHAnh29IkpWMDi+jqLvsoB+9XR20rwLvZVGe+mgTjCQ7Uuz6QvMKpNEtlnaj0X6FDRH6mpeoGKc/tkvgB/WB1baEULH6JVpkc2RT5X71Biuq2Qfg4spEyaRhloArEOLaNtbcziWg8xOYmlTHzQ==[/tex][tex=19.5x2.714]i0Pc5TjawqCmFkHHuR+ifRwXWF6/cD6z11R7FtYhlv0zAcCS+ykSM5x/U4xcUNRMGZrgT//GXK4Gnmt3FUomWCDUUMmOCHe+gY2qAV1mgqdzc+RiMBDPt0sZwxnzyxrYATZoZDyMphx2u4jW9hFqGirfrNwdwbk/nSQ+UuE0ISAar2TohTymp0Z42WBfpi/3[/tex][tex=18.857x2.786]lOXllVPSAOO5I/wOByZTgV51+S29hT1cYEgL3y7I8Fsaqdli35rRDKuIgU8hsesjjUQkzz4XRX2W+IBSwdWLpAXCU1Ax1Mrh+XiYNjrCizm4HkgWXcvijoaqe3fIcCwhfri8fMgfJi6Qxs4a+Gj4i2MdaHyyGk0zmmpCd8anfqqvMuWf3OxdmwlpG8gVhWzm[/tex][tex=27.643x2.929]jt3dUuwt2vSz329LzH+WcT21Uhv3Yunt1JGUG+D384FtzSbRYAtOK8RiuahV0XkFQGyJKZdvGIO+A4QJX2naoF4rHuHHI9kVFQBVjga4JmTGq3e663kW/UO6hZo3B98xUXwWviusWHLMOxlOzOx8d9w9/vLHAezSY16/63m9x4pG9QhHbkIB8zdFYYpnx6nQlB1ett7KZo3AEZ/nPqPb0VjbKZnon94y959KbqeVX56nr+tsuaThg4LuhTRAocn0VDvlVvPstVHR78Tm7lIG6A==[/tex][tex=12.071x2.643]jt3dUuwt2vSz329LzH+WcT21Uhv3Yunt1JGUG+D384FtzSbRYAtOK8RiuahV0XkFXjK1OFeXE+4QE7JVX4RRbAbd9obsOQ2sWDkOtvXB4SLEKp+0blMDd99l84bJsk0x[/tex]所以 [tex=18.357x2.929]ifsF+wWfiYrpFAHU6LOS0G3yxfTwFB5Xd5ErG1GArMCsG3urU3zDWXRK7+pHO9XeZxrhu4e3iDaHMAu88+UES2BObT5S/lXvowO8kWmISy1KZa8kNCTg76Rj5bzVxXjDzbKNLV6X3x7vZ320N+uAdw==[/tex][tex=19.214x2.714]k4ur+jkKscF5w19jmtpS93TjJhfeQs/6t+H5Hj67LynGhwaUGYB1IUNZwgSRCVQw8pVzQSaacE99uCeEIv5lSz90PdVZKKx5x4m3EkMK9VuvD+0J0jAL++o3pXYkyWfmns9jOgXLQmu8l9eprBGx1PZEwpmZkXybs7gf81iF1hAEg3QRgYb9vgMmkglDWd7O[/tex][tex=18.857x2.786]lOXllVPSAOO5I/wOByZTgV51+S29hT1cYEgL3y7I8FuHpPn3xLRpr3jNNePESmxDb23MZKz0wXFJ4W69ajYGr0SJA3RbEiiUQQf31a1c3iaGJdndGa4HLQGuaCjhAOm+UHJsEQBv9OhaF8JQORLn51qNHdKbUEGO+Ug45Q2UVHMvj70HyNksis1jq08RaNhs[/tex][tex=22.214x2.929]zNGUQp/lqk5gzA82/gaxCkv10ShZochvWFT1R8M61uORSuBH8sPKpb7SHzZZpTUgIH8DnE2a7VRVza7SKReRb/vPDSiFzwmME2GIJnUq/M+eZzIkleclavkNGb43HTtpNnAJJHBiS/Cl1FVwcZsEFfQwc6r0NgKIGCx67byzY4njJ7pHdVpIljPXflLJesG8[/tex]于是，[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 的傅里叶级数展开式为[tex=22.857x3.357]HIuSN7EzzwZ1HDWWExMyiVPxTb8GFzO50kQmF+KagIs2C6Xk56w+MnjR1weTjJZpQ5SHMso+uzJUQ8WnB2h8LXjMEyPzoMXnZLAGAbxSsXs+M7iDLL5o81ZjRs+aHJqZ+sSyA7h8wclXk/S4tHNW1Nax8LRvEJ70ZU0fyWT2yXeTvf11tlvDYVJ+fAhkCr45[/tex][tex=6.0x1.357]Ly/g9qGSH3cldzKxbkM1jnM8hUSnidCpJHbtcCBeFDc=[/tex] 且 [tex=10.643x1.357]u0XyfOQVeCjJ85hCJsHQ71EiHMjYqc+m976s0AfVGxY=[/tex]
    广告招租

    举一反三

    内容

    • 0

      下列周期函数[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]的周期为[tex=1.071x1.0]cWYnFY7tUlCT6WhMhv7goA==[/tex],试将[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]展开成傅里叶级数，如果[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]在[tex=3.071x1.357]dI/zQ2dAuab0sI9V1YLd+w==[/tex]上的表达式为：（2）[tex=9.857x1.5]pRJ95vWGjr1f90QgKzUvPeOQo4NAF+TvdpFQUXXdEgWX1T3yQcFbyRAQWVPZ9iHG[/tex]

    • 1

      下列周期函数[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]的周期为[tex=1.071x1.0]cWYnFY7tUlCT6WhMhv7goA==[/tex],试将[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]展开成傅里叶级数，如果[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]在[tex=3.071x1.357]dI/zQ2dAuab0sI9V1YLd+w==[/tex]上的表达式为：（1）[tex=11.286x1.5]5U9GdbHJKDgjuFkXJSrzULRfnXQYmtRNhThBBROPBwD9mXcghteFDeHwfjXFAdiC[/tex]

    • 2

      将下列以[tex=1.071x1.0]tieuzjBYrMcmxP3HXZSPGQ==[/tex]为周期的函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]展开为傅里叶级数，如果[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=2.929x1.357]QpSc4Vs3d1MTNQAH70ziEw==[/tex]上的表达式：[tex=11.286x1.5]uoK9dXTY5b+zhHj119y5pCgzedituUCxRZojcLgLEJHLEJv3ATnVkUij7MXL+UY/[/tex].

    • 3

      将下列以[tex=1.071x1.0]tieuzjBYrMcmxP3HXZSPGQ==[/tex]为周期的函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]展开为傅里叶级数，如果[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=2.929x1.357]QpSc4Vs3d1MTNQAH70ziEw==[/tex]上的表达式：[tex=11.071x1.5]IJwuJNbSgcLpUSCQjZhLKBJRwnnW1lXjwfuv04S+mWv3dyXfEVmq9L4aeKPnzkK6[/tex].

    • 4

      将下列以[tex=1.071x1.0]tieuzjBYrMcmxP3HXZSPGQ==[/tex]为周期的函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]展开为傅里叶级数，如果[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=2.929x1.357]QpSc4Vs3d1MTNQAH70ziEw==[/tex]上的表达式：[tex=9.714x1.357]j0ikBUEGw4d2AEflw2o0Ie2DTZ7v5Ty0vqhh7iBref2PI92JfJwAF/7b4kOXYelP[/tex].