Compact expressions for the magnetoresistance and the electron/hole density of states under the application of magnetic fields

The density of states of electron or hole systems under the application of external magnetic fields comprises an infinite sum of Landau levels (LLs), which in practical calculations is approximated by a finite sum. Here it is shown a mathematical expression that can be employed in place of these sums with the advantage of shorter computational time. A simplified expression for the corresponding magnetoresistance is also derived.