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Deriving tan power series

  1. Aug 27, 2010 #1
    How can the tan power series be derived from the sin and cos power series?
    Where do the Bernoulli numbers come in?
  2. jcsd
  3. Aug 27, 2010 #2
  4. Aug 27, 2010 #3
    I was expecting something yucky, and this doesn't disappoint...

    Thanks for the link :)
  5. Sep 2, 2010 #4
    Piano man. Here is a link in http://www.voofie.com/concept/Mathematics/" [Broken] that you maybe interested.

    http://www.voofie.com/content/117/an-explicit-formula-for-the-euler-zigzag-numbers-updown-numbers-from-power-series/" [Broken]

    I derived the power series of the function sec x + tan x. For the tan x power series, you just take the odd terms from the expansion, since tan x is an odd function. While sec x corresponds to the even terms from the power series, as sec x is even.

    It doesn't really show how Bernoulli numbers enter the expression, but it derives an explicit form for Bernoulli numbers.
    Last edited by a moderator: May 4, 2017
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