How to find the transfer function (or the gain) of the following circuit?
Can we short circuit R2 since there cannot be any input current?

 

If this is an ideal opamp no current will flow in R2 so I would say yes. However are you sure you have drawn this correct. As your drawing looks very simlar to a Sallen and Key filter section
http://www.ti.com/lit/an/sloa024b/sloa024b.pdf

 

Yes - I agree with t06afre.
However, in case of a true Sallen-Key lowpass (with C2 shifted to the non-inv. opamp input) the resistor R2, of course, must NOT be cancelled.

 

Thank you all. The schematic was wrong. Here is the correct one and I was able to solve that.







Solving procedure,
Apply KCL at V1
Apply KCL at V2
Remove V1 from above two equations and find V2-----(A)
Apply KCL at V3 and find V3----(B)
Apply Golden rules V2=V3
Make (A)=(B) and find (Vout/Vin) ratio from it.

 

Fine - that`s exactly the way I would solve the problem.