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7 Error Functions, Dawson’s and Fresnel IntegralsComputation

§7.22 Methods of Computation

  1. §7.22(i) Main Functions
  2. §7.22(ii) Goodwin–Staton Integral
  3. §7.22(iii) Repeated Integrals of the Complementary Error Function
  4. §7.22(iv) Voigt Functions
  5. §7.22(v) Other References

§7.22(i) Main Functions

The methods available for computing the main functions in this chapter are analogous to those described in §§6.18(i)6.18(iv) for the exponential integral and sine and cosine integrals, and similar comments apply. Additional references are Matta and Reichel (1971) for the application of the trapezoidal rule, for example, to the first of (7.7.2), and Gautschi (1970) and Cuyt et al. (2008) for continued fractions.

§7.22(ii) Goodwin–Staton Integral

See Goodwin and Staton (1948).

§7.22(iii) Repeated Integrals of the Complementary Error Function

The recursion scheme given by (7.18.1) and (7.18.7) can be used for computing inerfc(x). See Gautschi (1977a), where forward and backward recursions are used; see also Gautschi (1961).

§7.22(iv) Voigt Functions

The computation of these functions can be based on algorithms for the complementary error function with complex argument; compare (7.19.3).

§7.22(v) Other References

For a comprehensive survey of computational methods for the functions treated in this chapter, see van der Laan and Temme (1984, Ch. V).