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There is a huge field of asymptotic expansions and such over the real and complex fields (see Bender and Orszag, or Copson, or Whittaker and Watson). How different is the theory over p-adic fields? And is there a good introduction, with lots of examples, somewhere?

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    $\begingroup$ I do not know of any intro on this... but/and, having thought about the archimedean case (!?!) in recent years, I wonder what things you're wanting... $\endgroup$ Jun 9, 2015 at 0:40
  • $\begingroup$ @paulgarrett Perhaps asymptotic expansions for functions satisfying p-adic differential equations? $\endgroup$
    – Kimball
    Jun 9, 2015 at 3:38
  • $\begingroup$ @Kimball I would certainly not say no anything on that, but my original motivation is estimating integrals (in my case, over $p$-adic Lie groups, but that has a lot of extra baggage, so it would be good to know if there were anything like steepest descent, stationary phase, or whatever) $\endgroup$
    – Igor Rivin
    Jun 9, 2015 at 15:38

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