Digital Library of Mathematical Functions
About the Project
NIST
7 Error Functions, Dawson’s and Fresnel IntegralsComputation

§7.23 Tables

Contents

§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 \mathop{\mathrm{erf}\/}\nolimits x, (2/\sqrt{\pi})e^{{-x^{2}}}, x\in[0,2], 10D; (2/\sqrt{\pi})e^{{-x^{2}}}, x\in[2,10], 8S; xe^{{x^{2}}}\mathop{\mathrm{erfc}\/}\nolimits x, x^{{-2}}\in[0,0.25], 7D; 2^{n}\mathop{\Gamma\/}\nolimits\!\left(\frac{1}{2}n+1\right)\mathop{\mathrm{i}% ^{{n}}\mathrm{erfc}\/}\nolimits\!\left(x\right), n=1(1)6,10,11, x\in[0,5], 6S; \mathop{F\/}\nolimits\!\left(x\right), x\in[0,2], 10D; x\mathop{F\/}\nolimits\!\left(x\right), x^{{-2}}\in[0,0.25], 9D; \mathop{C\/}\nolimits\!\left(x\right), \mathop{S\/}\nolimits\!\left(x\right), x\in[0,5], 7D; \mathop{\mathrm{f}\/}\nolimits\!\left(x\right), \mathop{\mathrm{g}\/}\nolimits\!\left(x\right), x\in[0,1], x^{{-1}}\in[0,1], 15D.

  • Abramowitz and Stegun (1964, Table 27.6) includes the Goodwin–Staton integral \mathop{G\/}\nolimits\!\left(x\right), x=1(.1)3(.5)8, 4D; also \mathop{G\/}\nolimits\!\left(x\right)+\mathop{\ln\/}\nolimits x, x=0(.05)1, 4D.

  • Finn and Mugglestone (1965) includes the Voigt function \mathop{H\/}\nolimits\!\left(a,u\right), u\in[0,22], a\in[0,1], 6S.

  • Zhang and Jin (1996, pp. 637, 639) includes (2/\sqrt{\pi})e^{{-x^{2}}}, \mathop{\mathrm{erf}\/}\nolimits x, x=0(.02)1(.04)3, 8D; \mathop{C\/}\nolimits\!\left(x\right), \mathop{S\/}\nolimits\!\left(x\right), x=0(.2)10(2)100(100)500, 8D.

§7.23(iii) Complex Variables, z=x+iy

  • Abramowitz and Stegun (1964, Chapter 7) includes \mathop{w\/}\nolimits\!\left(z\right), 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 \mathop{\mathrm{erf}\/}\nolimits z, x\in[0,5], y=0.5(.5)3, 7D and 8D, respectively; the real and imaginary parts of \int_{x}^{\infty}e^{{\pm it^{2}}}dt, (1/\sqrt{\pi})e^{{\mp i(x^{2}+(\pi/4))}}\int_{x}^{\infty}e^{{\pm it^{2}}}dt, 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 \mathop{\mathrm{erf}\/}\nolimits z and \mathop{w\/}\nolimits\!\left(z\right) (the table on page 406 of this reference is for \mathop{w\/}\nolimits\!\left(z\right), not for \mathop{\mathrm{erfc}\/}\nolimits z), 11S.

  • Zhang and Jin (1996, p. 642) includes the first 10 zeros of \mathop{\mathrm{erf}\/}\nolimits z, 9D; the first 25 distinct zeros of \mathop{C\/}\nolimits\!\left(z\right) and \mathop{S\/}\nolimits\!\left(z\right), 8S.

© 2010–2013 NIST / Privacy Policy / Disclaimer / Feedback; Version 1.0.6; Release date 2013-05-06 Math-Image version (See MathML) . A Printed Companionis available.