The analysis of the present paper shows that in the case of |zph|c series solution, although does not converge outside the convergence circle determined by the singular point zph, is an asymptotic power series so long as 1/λ is less than 0.63+3μ+(1/Λ1) 1/Λ1, where 1/Λ1=min(|z|,1);μ+(x)=(1-2μ*x)μ*.