Error Function and Complementary Error Function Definitions - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 445

Appendix8

Error Function and
Complementary Error
Function Definitions

The “error function” is defined as

2
√ π

x

e − y 2 d y .

erf (x) =

0

The “complementary error function” is defined as

erfc (x) = 1 − erf (x) .

Some characteristics of the error functions are given below:

= =

erf ( 0 ) 0 erfc ( 0 ) 1

∞ = ∞ =

erf ( ) 1 erfc ( ) 0

erf ( −∞ ) =− 1

erfc ( − x) =− erf (x) erfc ( − x) = 1 − erf (x) = 1 + erf (x) = 2 − erfc (x)

The following is a partial table of error function values. For a complete tabulation see
Abramovitz, M. and Stegun, I.A. (1965) Handbook of Mathematical Functions .New
York: Dover Publications.

x erf( x )

0.00 0.0000000000

0.02 0.0225645747

0.04 0.0451111061

0.06 0.0676215944

0.08 0.0900781258

0.10 0.1124629160

0.20 0.2227025892

0.30 0.3286267595

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