p>

<!-- primary refs:
  http://en.wikipedia.org/wiki/Pendulum_%28mathematics%29
  http://kr.cs.ait.ac.th/~radok/math/mat6/calc81.htm
  http://books.google.com/books?id=xWrJlTIYl_IC&pg=PA280&lpg=PA280&dq=pendulum+elliptic+integrals&source=web&ots=zas9k5qVc0&sig=Tz-OwdqS84VPM2I_pZbtaspVZNk#PPA280,M1 (Computational Physics: Problem Solving with Computers by Rubin H. Landau, Cristian C. Bordeianu, p.280)
  http://en.wikipedia.org/wiki/Binomial_theorem
  http://mathworld.wolfram.com/EllipticIntegraloftheFirstKi