Computation of Complex Scorer Functions
نویسندگان
چکیده
Two Fortran 77 routines for the evaluation of Scorer functions of complex arguments Gi(z), Hi(z) and their derivatives are presented. The routines are based on the use of quadrature, Maclaurin series and asymptotic expansions. For real z comparison with a previous code by A.J. MacLeod (J. Comput. Appl. Math. 53 (1994)) is provided. 2000 Mathematics Subject Classification: 33C10, 65D20, 65D32, 30E10.
منابع مشابه
On nonoscillating integrals for computing inhomogeneous Airy functions
Integral representations are considered of solutions of the inhomogeneous Airy differential equation w′′ − z w = ±1/π. The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions are used to confine the discussion to one function and to a certain sector in the complex plane. By using steepest descent methods from asymptotics, the standar...
متن کاملAsymptotic formulae for the Lommel and Bessel functions and their derivatives
We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the same method, we obtain previously known approximate representations of the Nicholson type for Bessel functions and their first derivatives. We study also for ...
متن کاملOn the zeros of the Scorer functions
Asymptotic approximations are developed for zeros of the solutions Gi(z) and Hi(z) of the inhomogeneous Airy differential equation w′′ − zw = ± 1 π . The solutions are also called Scorer functions. Tables are given with numerical values of the zeros. 2000 Mathematics Subject Classification: 33C10, 41A60, 30E10, 30C15.
متن کاملComputation of Trigonometric Functions by the Systolic Implementation of the CORDIC Algorithm
Trigonometric functions are among the most useful functions in the digital signal processing applications. The design introduced in this paper computes the trigonometric functions by means of the systolic arrays. The method for computing these functions for an arbitrary angle, , is the CORDIC algorithm. A simple standard cell is used for the systolic array. Due to the fixed inputs, in some...
متن کاملComputation of Trigonometric Functions by the Systolic Implementation of the CORDIC Algorithm
Trigonometric functions are among the most useful functions in the digital signal processing applications. The design introduced in this paper computes the trigonometric functions by means of the systolic arrays. The method for computing these functions for an arbitrary angle, , is the CORDIC algorithm. A simple standard cell is used for the systolic array. Due to the fixed inputs, in some...
متن کامل