Generalizations of Laplace's Method

Retention of just the first term in this series produces the previous approximation to Z(x) for large x, namely

The corresponding contribution from the second term is (2.02) multiplied by xaO(x-'1'). From the next term we obtain (2.02) times x ~ " o ( x - ~ ' ~ ~ ) , and so on. In consequence, the original approximation should continue to apply, provided that pa < v.