• 2022-06-15
    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]
  • 解:[tex=12.0x2.786]Y2RoxqNCucSS0FRTPNZyMNfNsbJbZ6QxuCYhe1jnDokTB5CQZCUPugvorP9922uIlZpGsa2vlP9ZEvWgYQC60+DM6kAkAtPYM0bzByCEVeixCgi4UMWKgGZX5AV93EtG[/tex];[tex=20.214x14.571]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[/tex]故  [tex=10.071x2.929]U3pQCQGmzemByYoGPrYbeO/7SRfUQyx2UwSZ9c7gynDp2Z6GOD0Xcc+Bji/uK6AefbR4HQQb6wk2E5JkxxYfbr4y4e18Q/ZJcmL8w5WAHz2T/JMaOdqdrZy4+VDFlgV5[/tex][tex=5.5x1.357]J4R2lc1jx1bKYLWqDeRreg==[/tex];用分部积分法得[tex=10.5x2.714]BHWptzUDCgkM5U2iAnIUov9IsYcDkBVlY+l72O36PNMEt7sh3TDQqrxbmW0hW3zz2ZZ50uwcredJG8yNCttLYQ==[/tex][tex=12.929x2.929]h3aG/tSsUxSCQsY1veHGYNg8my0GEwXlTa8sX2MDucjt5vGYdzUzsfNgkF6qn6tWDE4RG7MfDFsbrAvgNkFuWxopjsG0hC5N6d14CfZvHNkJcrXnBYqTzDT3N3GJREkNOdDxpzSMki1ZY3A+mUgy8A==[/tex][tex=5.071x1.357]6nRiNACHIpJSZs4jcb0VbA==[/tex][tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]满足收敛定理的条件,而在[tex=5.0x1.357]YeOFs/TVcmW7kLoGKYugdQ==[/tex]处不连续[tex=3.214x1.357]WDvdFYgPHPuHYmrJ4qucMg==[/tex],故[tex=8.857x2.143]WpGo8UNPB9HxpxCyTQdz6sWEIhjfveOBdlb7Kr27pMywkgzZjV1NVT5Ue6Wh1No8HjO8BH272JYydWe+hUFN7A==[/tex][tex=14.071x2.714]EcyyKUHjEocXLsOiCiRSifEtPC/1eEJZwMe2Y9dXt7Q8OiOGY7zNVfC/GathLrYZr9zvvwt0L2v264NVSMoSqKth/LtK3/CHucH+UMa0ZcU=[/tex],[tex=7.929x1.357]6say0LQreJgqqQHiGEk02T85Xcs8jyNToIZud62Shxc=[/tex]。

    举一反三

    内容

    • 0

      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=9.857x1.5]Trp+Jj+ULSq36eDS/zm3sVxS6ArXCD/crKgNin7oQZzVR8JTs2/x8gvT6PLx2+33[/tex].

    • 1

      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].

    • 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=11.071x1.5]IJwuJNbSgcLpUSCQjZhLKBJRwnnW1lXjwfuv04S+mWv3dyXfEVmq9L4aeKPnzkK6[/tex].

    • 3

      证明:次数>0 且首项系数为 1 的多项式[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]是一个不可约多项式 的充分必要条件是,对任意多项式[tex=1.857x1.357]QPi3lZKJ+q/B5QY5cuDuQg==[/tex]必有(f(x), g(x))=1,或者对某一正整数[tex=6.0x1.357]bR39wf/Hz75eMrt08Xqk8wt4bXTUCgLbWgBjqC5Zmko=[/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].