512
Appendix C Useful Theoretical Approaches and Formulas
The integral in above expression can be evaluated as (Prudnikov et aZ., 1981):
foG exp [- ( ~ r -b 2 ] db v: {exp (20) [erf (c + ~) - 1] +
+ exp( - 2a) [erf (C - ~) + I]} ,
(C.172)
where error function erfx(x) is given by:
2 (X 2
erf(x) = ,j7r Jo e- t dt.
(C.173)
Tables for error function values may be found in any standard mathematical
tables (for example, Abramowitz and Stegun, 1975).
For practical calculation, the following approximation, suggested by Abramowitz and Stegun (1975), provides sufficiently accurate results:
(C.174)
in which:
t
l;px; p = 0.4707
., ~ 0.74785 }.
(C.175)
0.34802; a2 = -0.09588;