ABSTRACT
Chapter 11 we derive the same uniform asymptotic approximations in another way, applicable when Z(a,x) satisfies a differential equation of appropriate type.
12 Anger Functions of Large Order
12.1 In Chapter 3, Exercise 7.2, we stated the following asymptotic approximations for the functiont
in three cases when a is real and fixed, and v tends to infinity through positive real values:
These results are obtainable by the method of Laplace: when a > 1 the interval of integration contains no saddle points; when a = 1 there is a double saddle point at the endpoint t = 0; when 0 < a < 1 there is a simple saddle point interior to the interval of integration.
