第二类变型Bessel函数的Chebyshev逼近

基金项目: 上海市科技发展基金资助项目(98JC14032);上海市重点学科建设基金资助项目

Chebyshev Approximation of the Second Kind of Modified Bessel Function of Order Zero

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China

摘要: 第二类变型Bessel函数Kn(z)在自变量趋于无穷时就是指数变小的，使用多项式逼近的方法求解往往误差很大．采用指数变换和J.P.Boyd的有理Chebyshev多项式计算第二类变型Bessel函数，得到了令人满意的在较大范围内有效的解．
- 第二类变型Bessel函数 /
- 指数变换 /
- 有理Chebyshev多项式
Abstract: The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J. P. Boyd's rational Chebyshev basis.
- second kind of modified Bessel function of order zero /
- exponential transformation /
- rational Chebyshev basis

[1]	Amos D E.Computation of modified Bessel functions and their ratios[J].Math Comp,1974,28(24):239—251. doi: 10.1090/S0025-5718-1974-0333287-7
[2]	Campbell J B.Bessel functions In(z) and Kn(z) of real order and complex argument[J].Comput Phys Comm,1981,24(1):97—105. doi: 10.1016/0010-4655(81)90109-0
[3]	Gautschi W,Slavik J.On the computation of modified Bessel function ratios[J].Math Comp,1978,32(143):865—875. doi: 10.1090/S0025-5718-1978-0470267-9
[4]	Kerimov M K,Skorokhodov S L.Calculation of modified Bessel functions in the complex domain[J].U S S R Comput Math and Math Phys,1984,24(3):15—24. doi: 10.1016/0041-5553(84)90038-7
[5]	Segura J ,de Cordoba Fernandez P, Ratis Yu L.A code to evaluate modified Bessel functions based on the continued fraction method[J].Comput Phys Comm,1997,105(2/3):263—272. doi: 10.1016/S0010-4655(97)00069-6
[6]	Thompson I J,Barnett A R.Modified Bessel functions In(z) and Kn(z) of real order and complex argument,to selected accuracy[J].Comput Phys Comm,1987,47(4):245—257. doi: 10.1016/0010-4655(87)90111-1
[7]	Yoshida T,Ninomiya I.Computation of Bessel functions Kn(z) with complex argument by tau method[J].J Inform Process,1974,14(1):32—37.
[8]	Luke Y L.The Special Functions and Their Approximations[M].New York:Academic Press,1969.
[9]	Boyd J P.Orthogonal rational function on a semi-infinite[J].Journal of Computational Physics,1987,70:63—88. doi: 10.1016/0021-9991(87)90002-7