Algorithm 723: Fresnel integrals

ABSTRACT

An implementation of approximations for Fresnel integrals and associated functions is described. The approximations were originally developed by W. J. Cody, but a Fortran implementation using them has not previously been published.

REFERENCES

• 1: ABRAMOWrTZ, M., Ar~U STEGUN, I. 1966. Handbook of Mathematical Functions. Appl. Math. Ser. 55, National Bureau of Standards.
• 2: BULIRSCH, R. 1967. Numerical calculation of the sine, cosine and Fresnel integrals. Numer. Math. 9, 380-385.
• 3: CODY, W.J. 1968. Chebyshev approximations for the Fresnel integrals. Math. Comput. 22, 450-453, plus microfiche supplement.
• 4: HEM~R, P. W., Ed. 1981. NUMAL, Numerical Procedures in Algol 60 MC Syllabus 47.6, Mathematisch Centrum, Amsterdam.
• 5: HERSHEY, A.V. 1971. Approximations of Functzons by Sets of Poles. Internal report TR-2564, Naval Weapons Laboratory, Dahlgren, Va.
• 6: MORRis, A. H., JR. 1990. NSWC Library of Mathematics Subroutznes. Internal report NSWC TR 90-21, Naval Surface Warfare Center, Dahlgren, Va., Jan.
• 7: N~METH, G. 1965. Chebyshev expansions for Fresnel integrals. Numer. Math. 7, 310-312.
• 8: RICE, J.R. {1965}. On the conditioning of polynomial and rational forms. Numer. Math. 7, 426 435.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
          Subjects: Rational approximation

Additional Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Certification and testing

General Terms:
Algorithms

Keywords:
special functions