what is the input impedance of a transistor (bjt)
...not "something like (R1||R2||Rpi)". This is, of ocurse, already the correct expression for the dynamic input resistance (as can be derived from the diagram). Note that it would be more correct to write rpi instead of Rpi in order to clearly disinguish between dynamic and static resistances.

The dynamic resistance rpi is given by the inverse slope of the input chracteristic IB=f(VBE). Hence, we have rpi=d(VBE)/d(IB)=d(VBE)*B/d(IC). 

Because d(VBE)/d(IC)=1/gm we can write rpi=B/gm=B/(IC/VT)=(B*VT)/IC.

B=DC current gain, gm=transconductance, VT=temperature voltage, IC=DC collector current.   

Example: For B=200, IC=2mA and VT=26mV we get rpi=2.6 kOhm.