Entropy Function for 4-Charge Extremal Black Holes in Type IIA   Superstring Theory
  We calculate the entropy of 4-charge extremal black holes in Type IIA supersting theory by using Sen's entropy function method. Using the low energy effective actions in both $10D$ and 4D, we find precise agreements with the Bekenstein-Hawking entropy of the black hole. We also calculate the higher order corrections to the entropy and find that they depend on the exact form of the higher order corrections to the effective action. 
Rong-Gen Cai, Da-Wei Pang