1. If
then F maps the unit disc conformally onto the interior of a regular polygon with n sides and perimeter
2. The elliptic integrals K and Kdefined for 0
satisfy various interesting identities. For instance:
(c) Show that for 0
where F the hypergeometric series. [Hint: This follows from the integral representation for F given in Exercise 9, Chapter 6.]
Exercise 9
Show that
where γ is Euler’s constant.
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