Computation of Bessel and Airy functions and of related Gaussian quadrature formulae

BIT Numerical Mathematics

Volumn 42, Issue 1, 2002, Pages 110-118

  Gautschi, Walter ^a  

^a Purdue University   (United States)

Author keywords

Airy function; Gaussian quadrature; Modified Bessel function

Indexed keywords

EID: 0042920795     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021974203359     Document Type: Article

References (12)

1. M. Abramowitz and I. A. Stegun (eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, NBS Applied Mathematics Series, Vol. 55, U.S. Government Printing Office, Washington, DC, 1964.
2. W. Gautschi, How and how not to check Gaussian quadrature formulae, BIT, 23 (1983), pp. 209-216.
3. W. Gautschi, Algorithm 726: ORTHPOL - A package of routines for generating orthogonal polynomials and Gauss-type quadrature rules, ACM Trans. Math. Software, 20 (1994), pp. 21-62.
4. W. Gautschi, Orthogonal polynomials: applications and computation, Acta Numerica, 5 (1996), pp. 45-119.
5. R. G. Gordon, New method for constructing wavefunctions for bound states and scattering, J. Chem. Phys., 51 (1969), pp. 14-25.
6. R. G. Gordon, Constructing wavefunctions for nonlocal potentials, J. Chem. Phys., 52 (1970), pp. 6211-6217.
7. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press, San Diego, CA, 2000.
8. D. W. Lozier and F. W. J. Olver, Numerical evaluation of special functions, in Mathematics of Computation 1943-1993: A half-century of computational mathematics, Vancouver, BC, 1993, W. Gautschi, ed., Proc. Sympos. Appl. Math., Vol. 48, Amer. Math. Soc., Providence, RI, 1994, pp. 79-125.
9. Z. Schulten, D. G. M. Anderson, and R. G. Gordon, An algorithm for the evaluation of the complex Airy functions, J. Comput. Phys., 31 (1979), pp. 60-75.
10. N. M. Temme, On the numerical evaluation of the modified Bessel function of the third kind, J. Comput. Phys., 19 (1975), pp. 324-337.
11. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge University Press, Cambridge, 1958.
12. R. Wong, Quadrature formulas for oscillatory integral transforms, Numer. Math., 39 (1982), pp. 351-360.