设函数

Raw JSON

{
  "kind": 1,
  "id": "6922c692cd7f18f38c9120fef8107ca182fc676852a82f12ed0b7868505dfd4f",
  "pubkey": "8925425a9130192b987239987433a6998f4557359a404b5a41940aa070dddd1c",
  "created_at": 1772453053,
  "tags": [
    [
      "alt",
      "A short note: 设函数\n \nf(x) = \\frac{\\sin(\\pi x)}{x^2 - 2x + 2} + e^..."
    ],
    [
      "e",
      "1436244c551fc7d9e27c3fcb3e3e1318cf41e74f88b3e3616f76e910a5e1c260",
      "wss://nostr-03.dorafactory.org/",
      "root",
      "8925425a9130192b987239987433a6998f4557359a404b5a41940aa070dddd1c"
    ],
    [
      "e",
      "27b4abdef730020cde79e11cfb8ab0a12270f12c24d673f83cad6a178ccde9fd",
      "wss://relay.nostr.net/",
      "reply",
      "8888888890493e0c6a6e4a24ae3319a0d7fc595ca3d8e5cae19954e1139008d3"
    ],
    [
      "p",
      "461b1eae716b0bf2de4307d52c3338c09010e7704566afba29f33ad54289a11a",
      "wss://relay.damus.io/"
    ],
    [
      "p",
      "8925425a9130192b987239987433a6998f4557359a404b5a41940aa070dddd1c",
      "wss://relay.artiostr.ch/"
    ],
    [
      "p",
      "8888888890493e0c6a6e4a24ae3319a0d7fc595ca3d8e5cae19954e1139008d3",
      "wss://relay.damus.io/"
    ]
  ],
  "content": "设函数\n \nf(x) = \\frac{\\sin(\\pi x)}{x^2 - 2x + 2} + e^{-x^2}\\ln\\left(1 + \\frac{1}{1+x^2}\\right)\n \n定义\n \nI = \\lim_{n\\to\\infty} \\int_{-n}^{n} \\left( f(x) - \\frac12 f''(x) \\right) \\arctan\\left(e^x\\right) dx\n\n再令\n \nJ = \\sum_{k=1}^{\\infty} \\frac{(-1)^{k+1}}{k} \\int_{0}^{1} \\frac{x^{k-1}}{\\sqrt{1 - x^2}} dx\n \n求\n\nK = I + J\n\n并给出 K的精确值。",
  "sig": "214a6334cbf3728130f9f98957752be9605b86bc2c3cf05e7b4c93806e49ad2aac998cd6e9b0f2b8410a0a0110aaaa1bff730c75e55eec6609d62d392b1e9780"
}