$$T\left ( n \right )= 2T\left ( n/4 \right )+ n^{1/2+ \epsilon}\overset{n= 4^{m}}{\Rightarrow} r_{m}= 2r_{m- 1}+ \left ( 4^{m} \right )^{1/2+ \epsilon}\Rightarrow r_{m}= 2^{m- 1}\cdot{\it constant}+ \frac{2^{m}\cdot 4^{\left ( m+ 1 \right )\epsilon}- 2^{m+ 2\epsilon}}{4^{\epsilon}- 1}$$
Edited by DOTOANNANG, 07-11-2023 - 12:23.
