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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.

16 votes
1 answer
2k views

What are some of the earliest examples of analytic continuation?

I'm wondering how Riemann knew that $\zeta(z)$ could be extended to a larger domain. In particular, who was the first person to explicitly extend the domain of a complex valued function and what was …
Mustafa Said's user avatar
  • 3,699
6 votes

Old books still used

Barry Simon and Michael Reed's classic volume on Functional Analysis (1981) is my one of my favorites. Ayoub, "An Introduction to the Analytic Theory of Numbers," (1963) is out of print but one of th …