论文信息 - Chebyshev expansions for Abramowitz functions

Chebyshev expansions for Abramowitz functions

Abstract The paper discusses the evaluation of the functions J n (x) =∫0∞t n exp(−t 2 −x⧸t)dt by using Chebyshev expansions. It is known that values of J n can be derived by a recurrence based on J 0 , J 1 and J 2 so only these functions are considered. Coefficients are derived which are accurate to 20 decimal places.

A. MacLeod | Allan J. Macleod

[1] Milton Abramowitz,et al. Evaluation of the Integral , 1953 .

[2] S. A. Beresnev,et al. Motion of a spherical particle in a rarefied gas. Part 2. Drag and thermal polarization , 1990, Journal of Fluid Mechanics.

[3] J. L. Schonfelder,et al. The production of special function routines for a multi‐machine library , 1976, Softw. Pract. Exp..

[4] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[5] C. W. Clenshaw. Chebyshev series for mathematical functions , 1962 .

[6] Raphael Aronson,et al. Theory and application of the Boltzmann equation , 1976 .

[7] L. Wayne Fullerton,et al. Portable Special Function Routines , 1976, Portability of Numerical Software.

[8] C Pescatore,et al. Evaluation of the integral ∫0∞tnexp(−t2−xt)dt , 1979 .