冪級數解ODE 收斂範圍疑問
（x^2+1)y"+xy'-y=0
上式若以冪級數求解，並以x=0為展開中心，則因0爲常點所以可用泰勒級數展開，因此可以y=Σa_n*x^n
這時候問題來了，因為每個無窮級數都要寫收斂範圍，可是這樣令的時候，收斂範圍我不知道怎麼求，總不會是+i -i吧
課本上收斂範圍是寫-1<x<1，可是我算不出來啊@@
-----
Sent from JPTT on my iPhone
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 61.221.58.4
※ 文章網址: https://www.ptt.cc/bbs/Grad-ProbAsk/M.1493087496.A.0A6.html
※ 編輯: bightw24261 (61.221.58.4), 04/25/2017 10:33:39
※ 編輯: bightw24261 (61.221.58.4), 04/25/2017 10:35:11
→
04/25 10:34, , 1F
04/25 10:34, 1F
→
04/25 10:35, , 2F
04/25 10:35, 2F
→
04/25 10:39, , 3F
04/25 10:39, 3F
→
04/25 10:39, , 4F
04/25 10:39, 4F
→
04/25 10:40, , 5F
04/25 10:40, 5F
→
04/25 10:40, , 6F
04/25 10:40, 6F
→
04/25 10:40, , 7F
04/25 10:40, 7F
→
04/25 10:46, , 8F
04/25 10:46, 8F
→
04/25 10:46, , 9F
04/25 10:46, 9F
→
04/25 10:51, , 10F
04/25 10:51, 10F
→
04/25 10:51, , 11F
04/25 10:51, 11F
→
04/25 10:52, , 12F
04/25 10:52, 12F
→
04/25 10:52, , 13F
04/25 10:52, 13F
→
04/25 11:00, , 14F
04/25 11:00, 14F
→
04/25 11:00, , 15F
04/25 11:00, 15F
→
04/25 11:00, , 16F
04/25 11:00, 16F
→
04/25 11:01, , 17F
04/25 11:01, 17F
→
04/25 11:01, , 18F
04/25 11:01, 18F
→
04/25 11:01, , 19F
04/25 11:01, 19F
→
04/25 11:02, , 20F
04/25 11:02, 20F
→
04/25 11:03, , 21F
04/25 11:03, 21F
→
04/25 11:18, , 22F
04/25 11:18, 22F