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On nonoscillating integrals for computing inhomogeneous Airy functions. (English) Zbl 0972.33004
Integral representations are considered of solutions of the inhomogeneous Airy differential equation w '' -zw=±1/π. The solutions of these equations are also known as Scorer functions. By using steepest descent methods from asymptotics, the standard integral representations of the Scorer functions are modified in order to obtain non-oscillating integrals for complex values of z. In this way stable representations for numerical evaluations of the functions are obtained. The methods are illustrated with numerical results.
MSC:
33C10Bessel and Airy functions, cylinder functions, 0 F 1
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
30E10Approximation in the complex domain
65D20Computation of special functions, construction of tables