§7.22 Methods of Computation

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

§7.22(i) Main Functions

Keywords:: Dawson’s integral, Fresnel integrals, auxiliary functions for Fresnel integrals, error functions
Referenced by:: ¶ ‣ §3.10(iii)
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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

Keywords:: Goodwin–Staton integral
Permalink:: http://dlmf.nist.gov/7.22.ii

See Goodwin and Staton (1948).

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

Keywords:: repeated integrals of the complementary error function
Permalink:: http://dlmf.nist.gov/7.22.iii

The recursion scheme given by (7.18.1) and (7.18.7) can be used for computing $\mathop{\mathrm{i}^{{n}}\mathrm{erfc}\/}\nolimits\!\left(x\right)$ . See Gautschi (1977a), where forward and backward recursions are used; see also Gautschi (1961).

§7.22(iv) Voigt Functions

Keywords:: Voigt functions
Permalink:: http://dlmf.nist.gov/7.22.iv

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

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