2.3 Verify the limiting behavior of Eq. (2.20). Hint: Use the elementary inequality log(1 − x) ≤ −x for 0 < x < 1, the elementary limit (1 + x∕????)

???? → ex as

???? → ∞, and Stirling’s formula

Γ(????) ∼ e−???? ????????− 1 2 (2????)

1 2 .