Hi,

> 1. Beta function that calculates the value of B(x,y) is present in 
> functions module gamma_functions.py. Should it remain there or be
> rewritten in the new class. 

It should be replaces by a the new class and of course extended.

> 2. What are branch cuts?

 http://en.wikipedia.org/wiki/Branch_cut#Branch_cuts

> and if I am creating a new class inside the
> same module should the value be true or false?

If in doubt, remove the variable.

> 3. The structure of the class should remain same as in
> gamma_function?

Probably yes as its a very similar function. Almost all
special function share most of their class structure.

> i.e I should start with fdiff and move on with other
> applicable operations ?

Yes, that would be a good start. See also:

 https://github.com/sympy/sympy/wiki/About-implementing-special-functions

Note to self: finish that article.

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