The deadlines ringing do remind that 3 months have flown past in a jiffy. Time to bid sayonara! Good times seem to roll by too soon, always; sad thing! Nevertheless it has been a great experience under a brilliant mentoring. The post has come up much later the previous one. Things have taken shape since then.

1. Ellipsoidal Harmonics:
 Ellipsoidal harmonic functions, the first kind; also known as Lames functions have been implemented in Cython and had been integrated with ufuncs.
 Ellipsoidal Harmonic function of the second kind and the calculation normalization constant for Lames function were implemented as .pyx files due to the involvement of global variables. The calculation of normalization constant was implemented in 2 different ways, using integration and using recurrence. Though recurrence seemed to be the more basic and faster way of implementation, the numerical stability wasn't that good; so we adopted integration.
The process involved many new things to me, like the integration of awesome LAPACK library, the speed and awesomeness of Cython etc!
The pull request is here: https://github.com/scipy/scipy/pull/3811
2. Hypergeometric functions:
The present implementation of hypergeometric functions is buggy. For real values of x, C implementation of the function from Cephes library has few errors while the FORTRAN implementation for complex values of x suffers with errors for much wider domain. There has been an attempt to re-implement the function in Cython and make it less ridden with errors. Though the shortage of time denied a bug-free implementation a few bugs have been removed successfully.
The implementation so far has been posted here

I would yet again stress on the fact that the flipping of bits this summer has been of great fun and well as a great skill and knowledge booster. Never was my summer so productive!

Signing off with loads of great memories and experiences
Janani