将[tex=2.857x1.0]lw6lAp/qSjxLWajfYtf5BA==[/tex]展为[tex=0.5x0.786]gdMkE6SnyZedYLxpUxdkaQ==[/tex]的幂级数.

2022-06-19

将[tex=2.857x1.0]lw6lAp/qSjxLWajfYtf5BA==[/tex]展为[tex=0.5x0.786]gdMkE6SnyZedYLxpUxdkaQ==[/tex]的幂级数.

答案：

因为[tex=2.857x1.0]lw6lAp/qSjxLWajfYtf5BA==[/tex]和[tex=3.0x1.0]jjAs5nrYoGytwlIG/SyV6A==[/tex]均在复平面上解析，将它们分别作为实部与虚部，利用欧拉公式，得[tex=24.5x6.214]ShzNtLiptBnyqZQQbDCJvS3HklB5KGE3X94GIaXH5yG4JvlvoFwSyApDhgjZIjSiQytpCK2JUzbq5OfDeBhza5mJ+8HlrQhj2AB0sKek6i7RnSY0wf0/EDC7229S0IZWi/ccggEkf0LFHezOtFY2Znfxm0ijAb9CN2PJmtCxFf2vzplhcNtOpLBIo/lgSaXWUImIDeFqJIlRmydkiyELLzcHPWCacDnQhnviNS0HVEsX65C+II4G+nQuwomsgLMpNRVdxwFtR9krfUBWcyw9j2K6ozGrKgZpvjFhUvv3VlZkg/ptmxl7Q3nRsqV7iFfp/SPoNPNuMqxHc9/pQmQ+S8IZrQpEXySR1lqr+JjS87IEHM7ByRdqVyxowwmqPojF[/tex].同理[tex=10.286x1.429]XlDvYl+xwXz2P603nepu7bFkFc8fXKq8aFdBTqygdc/lLPraVMA0savFsRdSqDba[/tex][tex=16.071x2.714]i1ARBCW3T2Xi0Sg4wAiw5FHroeAByv0xXjpUISpcqrbHqQnQ3wmebFKigTZjtJdeLu74ZenIwHp7KJpTswmtpnE2JBoQGRxolZVbOGiNhsTxEsHK9ubU+QkFi7O0UVsvIesGCL1nno9X4+9G/3cHdq0YMFE/gTN2/qNLoQQOcs4=[/tex].将两式相减后除以2，即得[tex=13.143x2.643]cN3sSk1wuS1er0UEuOdNpeBBE996jnK9t21stPKy9cebNv4zfU4/FClt1i/uU1qGjYeJRG/XtbNBOx5hFm/blrYbKSJ2ESzncfykbUopS9RbI//wgvJjzNSPoFE+8A1KjYucsWGeArWG2K/myl0Qqg==[/tex]，[tex=4.143x1.357]u9hHxB8frlL0qBsvXpu/kA==[/tex].将两式相加后除以2，即得[tex=13.286x2.714]EIuhJmr02RPpt90+o/MDqjsHVJ/095RKkdkV7L8NUogRi+BB03Lx5NSbP51tGvh4m0CbgbcbIvaHxEOjfIoK44c2ISfaZQ2nw7CO+GQ1GmRcrHlza9qxD6qd5DxgnSlSOAETdKN0aBYPxquL8KMXaA==[/tex]，[tex=4.143x1.357]u9hHxB8frlL0qBsvXpu/kA==[/tex].

举一反三

内容

0
将函数[tex=8.786x2.786]/LqTmimv1DBetnXYf1ppel9odHIAFEgXxE8DdjNN9uVDVWMmfvTPzGWtg2BdegxL[/tex] 展开成[tex=0.5x0.786]C7x+w8+jOPZzxFrGGne6Dw==[/tex]的真级数至含 [tex=1.0x1.214]yFat4COBgo7WTPaNshNYVeaf+oyrT5Pl5CmZzxzdlkI=[/tex]的项.
1
将函数[tex=8.786x2.786]/LqTmimv1DBetnXYf1ppel9odHIAFEgXxE8DdjNN9uVDVWMmfvTPzGWtg2BdegxL[/tex] 展开成[tex=0.5x0.786]C7x+w8+jOPZzxFrGGne6Dw==[/tex] 的m级数至含 [tex=0.929x1.214]nl3S1EsI5SJD93W5mL66nQ==[/tex]的项.
2
已知离散时间单位阶跃信号 [tex=2.0x1.357]iZD6NkhBJKglclpk41Y0Tg==[/tex]的 [tex=0.5x0.786]C4QYj735kvdXFh+j8eTFZg==[/tex] 变换为 [tex=6.286x2.429]6bHRnXEcE3YuYgsZEcLaS9iRCWd9qeKmCIv7GxEBSgA=[/tex]利用 [tex=0.5x0.786]gdMkE6SnyZedYLxpUxdkaQ==[/tex]变换的性质求下列信号的[tex=0.5x0.786]gdMkE6SnyZedYLxpUxdkaQ==[/tex] 变换 [tex=3.0x1.5]lcNYeOjHojd31JjlC3RNbQ==[/tex]
3
已知离散时间单位阶跃信号 [tex=2.0x1.357]iZD6NkhBJKglclpk41Y0Tg==[/tex]的 [tex=0.5x0.786]C4QYj735kvdXFh+j8eTFZg==[/tex] 变换为 [tex=6.286x2.429]6bHRnXEcE3YuYgsZEcLaS9iRCWd9qeKmCIv7GxEBSgA=[/tex]利用 [tex=0.5x0.786]gdMkE6SnyZedYLxpUxdkaQ==[/tex]变换的性质求下列信号的[tex=0.5x0.786]gdMkE6SnyZedYLxpUxdkaQ==[/tex] 变换 [tex=2.571x3.286]1mLHjxcun+rgXN/f39rje0IyX6K9VMlbGLe63DfbQjA=[/tex]
4
把函数 [tex=2.357x1.857]WUZfZR6Ot+pMzLu8uZlHhP5hasgoOcTypVE0BzDZRuY=[/tex] 展成 [tex=0.5x0.786]C7x+w8+jOPZzxFrGGne6Dw==[/tex] 的幂级数,并指出其收敛半径.