Polynomial approximations in the complex plane
Journal of Computational and Applied Mathematics
Complex polynomial approximation by the Lanczos &tgr;-method: Dawson's integral
Journal of Computational and Applied Mathematics
Numerical evaluation of airy functions with complex arguments
Journal of Computational Physics
Algorithm 715: SPECFUN–a portable FORTRAN package of special function routines and test drivers
ACM Transactions on Mathematical Software (TOMS)
Computations of the complex error function
SIAM Journal on Numerical Analysis
Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Numerical Analysis
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The Lanczos @t-method, with perturbations proportional to Faber polynomials, is employed to approximate the Bessel functions of the first kind J"v(z) and the second kind Y"v(z), the Hankel functions of the first kind H"v^(^1^)(z) and the second kind H"v^(^2^)(z) of integer order v for specific outer regions of the complex plane, i.e. |z| = R for some R. The scaled symbolic representation of the Faber polynomials and the appropriate automated @t-method approximation are introduced. Both symbolic and numerical computation are discussed. In addition, numerical experiments are employed to test the proposed @t-method. Computed accuracy for J"0(z) and Y"0(z) for |z| = 8 are presented. The results are compared with those obtained from the truncated Chebyshev series approximations and with those of the @t-method approximations on the inner disk |z| =