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7 Error Functions, Dawson’s and Fresnel IntegralsComputation

§7.23 Tables

  1. §7.23(i) Introduction
  2. §7.23(ii) Real Variables
  3. §7.23(iii) Complex Variables, z=x+iy
  4. §7.23(iv) Zeros

§7.23(i) Introduction

Lebedev and Fedorova (1960) and Fletcher et al. (1962) give comprehensive indexes of mathematical tables. This section lists relevant tables that appeared later.

§7.23(ii) Real Variables

  • Abramowitz and Stegun (1964, Chapter 7) includes erfx, (2/π)ex2, x[0,2], 10D; (2/π)ex2, x[2,10], 8S; xex2erfcx, x2[0,0.25], 7D; 2nΓ(12n+1)inerfc(x), n=1(1)6,10,11, x[0,5], 6S; F(x), x[0,2], 10D; xF(x), x2[0,0.25], 9D; C(x), S(x), x[0,5], 7D; f(x), g(x), x[0,1], x1[0,1], 15D.

  • Abramowitz and Stegun (1964, Table 27.6) includes the Goodwin–Staton integral G(x), x=1(.1)3(.5)8, 4D; also G(x)+lnx, x=0(.05)1, 4D.

  • Finn and Mugglestone (1965) includes the Voigt function H(a,u), u[0,22], a[0,1], 6S.

  • Zhang and Jin (1996, pp. 637, 639) includes (2/π)ex2, erfx, x=0(.02)1(.04)3, 8D; C(x), S(x), x=0(.2)10(2)100(100)500, 8D.

§7.23(iii) Complex Variables, z=x+iy

  • Abramowitz and Stegun (1964, Chapter 7) includes w(z), x=0(.1)3.9, y=0(.1)3, 6D.

  • Zhang and Jin (1996, pp. 638, 640–641) includes the real and imaginary parts of erfz, x[0,5], y=0.5(.5)3, 7D and 8D, respectively; the real and imaginary parts of xe±it2dt, (1/π)ei(x2+(π/4))xe±it2dt, x=0(.5)20(1)25, 8D, together with the corresponding modulus and phase to 8D and 6D (degrees), respectively.

§7.23(iv) Zeros

  • Fettis et al. (1973) gives the first 100 zeros of erfz and w(z) (the table on page 406 of this reference is for w(z), not for erfcz), 11S.

  • Zhang and Jin (1996, p. 642) includes the first 10 zeros of erfz, 9D; the first 25 distinct zeros of C(z) and S(z), 8S.