Ciro Santilli OurBigBook.com $£ Sponsor €¥ 中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件 邓家贵、低端人口、西藏骚乱
Essentially, defining an holomorphic function on any open subset, no matter how small, also uniquely defines it everywhere.
This is basically why it makes sense to talk about analytic continuation at all.
One way to think about this is because the Taylor series matches the exact value of an holomorphic function no matter how large the difference from the starting point.
Therefore a holomorphic function basically only contains as much information as a countable sequence of numbers.

Ancestors

  1. Analytic continuation
  2. Complex analysis
  3. Calculus
  4. Area of mathematics
  5. Mathematics
  6. Ciro Santilli's Homepage