Sharpe ratio of portfolio combining benchmark and actively managed portfolio

Can someone confirm if my understanding below is accurate?

Where:
SRc = Sharpe Ratio of combined portfolio
SRc* = Optimal Sharpe Ratio of combined portfolio
SRb = Sharpe Ratio of benchmark
IRp* = Optimal Information Ratio of actively managed portfolio
TC = Transfer Coefficient

Is it correct to say:
SRc^2 = SRb^2 + [TC^2 + IRp*^2] ?

And where TC = 1, the formula becomes:
SRc*^2 = SRb^2 + IRp*^2 ?

Thanks!