About the Project
NIST

Goodwin–Staton integral

AdvancedHelp

(0.001 seconds)

9 matching pages

1: 7.25 Software
§7.25(vi) ( x ) , G ( x ) , U ( x , t ) , V ( x , t ) , x
§7.25(vii) ( z ) , G ( z ) , z
2: 7.23 Tables
  • Abramowitz and Stegun (1964, Table 27.6) includes the GoodwinStaton integral G ( x ) , x = 1 ( .1 ) 3 ( .5 ) 8 , 4D; also G ( x ) + ln x , x = 0 ( .05 ) 1 , 4D.

  • 3: 7.2 Definitions
    §7.2(v) GoodwinStaton Integral
    7.2.12 G ( z ) = 0 e - t 2 t + z d t , | ph z | < π .
    4: 7.1 Special Notation
    The main functions treated in this chapter are the error function erf z ; the complementary error functions erfc z and w ( z ) ; Dawson’s integral F ( z ) ; the Fresnel integrals ( z ) , C ( z ) , and S ( z ) ; the GoodwinStaton integral G ( z ) ; the repeated integrals of the complementary error function i n erfc ( z ) ; the Voigt functions U ( x , t ) and V ( x , t ) . …
    5: 7.5 Interrelations
    7.5.13 G ( x ) = π F ( x ) - 1 2 e - x 2 Ei ( x 2 ) , x > 0 .
    6: 7.22 Methods of Computation
    §7.22(ii) GoodwinStaton Integral
    7: Software Index
    8: 7.12 Asymptotic Expansions
    §7.12(iii) GoodwinStaton Integral
    See Olver (1997b, p. 115) for an expansion of G ( z ) with bounds for the remainder for real and complex values of z .
    9: Bibliography G
  • E. T. Goodwin and J. Staton (1948) Table of 0 e - u 2 u + x d u . Quart. J. Mech. Appl. Math. 1 (1), pp. 319–326.