COMPUTING PROGRAMS FOR THE COMPLEX FRESNEL INTEGRAL

Abstract

The asymptotic series for the complex Fresnel integral with remainder is used in subroutines to evaluate the conventional Fresnel integrals and the probability integral. A series expansion with improved accuracy of calculation is used to evaluate the remainder. A rational polynomial approximation is developed for the complex Fresnel integral. The range of validity of the rational approximation is that part of the complex plane on the negative side which is bounded by the imaginary axis and is outside a circle of unit radius. The complex Fresnel integral correct to thirteen significant digits is tabulated at unit intervals in the argument.

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Document Details

Document Type
Technical Report
Publication Date
Nov 19, 1962
Accession Number
AD0289387

Entities

People

  • A. V. Hershey

Organizations

  • Naval Surface Warfare Center Dahlgren Division

Tags

Communities of Interest

  • Air Platforms
  • Weapons Technologies

DTIC Thesaurus Topics

  • Analytic Functions
  • Computational Science
  • Engineering
  • Engineers
  • Equations
  • Fluid Dynamics
  • Fresnel Integrals
  • Instructions
  • Integrals
  • Marine Engineering
  • Mathematics
  • Military Research
  • Naval Architecture
  • Polynomials
  • Precision
  • Probability
  • Sequences

Readers

  • Calculus or Mathematical Analysis