Texas Instruments TI-89 Tip List

erf
(
x
)
=
2
✜
¶
0
x
e
−t
2
dt
For x > -3 and x < 3, the error function looks like this:
erf(x) approaches 1 and -1 for large x and large -x, respectively. Also note that erf(-x) = -erf(x). The
complimentary error function erfc(x) is defined as
erfc(x) = 1 - erfc(x)
This function calculates erf(x) for all real x.
erf(x)
func
©(x) error function of x
©dburkett@infinet.com 13 nov 99
©x real and -1E-999 <= x <= 1E999
©Error +/- 1E-14.
when(x<0,⁻erf(⁻x),when(x<.84375,x+x*polyeval({⁻2.3763016656650⁻5,⁻5.77027029648
94⁻3,⁻2.8481749575599⁻2,⁻3.25042107247⁻1,1.2837916709551⁻1},x*x)/polyeval({⁻
3.9602282787754⁻6,1.3249473800432⁻4,5.0813062818758⁻3,6.5022249988767⁻2,3.97
91722395916⁻1,1},x*x),when(x<1.25,.84506291151047+polyeval({⁻2.1663755948688⁻3
,3.5478304325618⁻2,⁻1.108946942824⁻1,3.1834661990116⁻1,⁻3.722078760357⁻1,4.1
485611868375⁻1,⁻2.3621185607527⁻3},x-1)/polyeval({1.1984499846799⁻2,1.3637083
912029⁻2,1.2617121980876⁻1,7.1828654414196⁻2,5.4039791770217⁻1,1.06420880400
84⁻1,1},x-1),when(x<2.8571428571 429,1-1/x*ℯ^(⁻x*x-.5625+polyeval({⁻9.8143293441
691,⁻8.12874355063071,⁻1.84605092906712,⁻1.62396669462572,⁻6.23753324503261,
⁻1.055862622532341,⁻6.9385857270718⁻1,⁻9.8649440348471⁻3},1/x^2)/polyeval({⁻6
.0424415214858⁻2,6.5702497703193,1.08635005541782,4.29008140027572,6.45387271
733272,4.34565877475232,1.37657754143522,1.96512716674391,1},1/x^2)),when(x<
5.518,1-1/x*ℯ^(⁻x*x-.5625+polyeval({⁻4.83519191608652,⁻1.02509513161113,⁻6.375
66443368392,⁻1.60636384855822,⁻1.77579549177551,⁻7.9928323768052⁻1,⁻9.864942
9247001⁻3},1/x^2)/polyeval({⁻2.24409524465861,4.74528541206962,2.553050406433
23,3.1998582195086 3,1.53672958608443,3.25792512996572,3.03380607434821,1},1
/x^2)),1)))))
Endfunc
This function is accurate to full machine precision for all arguments. The algorithm is taken from
module ERF in the FDLIBM package. This link provides the algorithm details:
http://gams.nist.gov/serve.cgi/Module/FDLIBM/ERF/13299/
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Texas Instruments TI-89 Specifications

General

Display size (HxV)	100 x 160 mm
Memory type	639K FLASH ROM, 188K bytes RAM
Compatible operating systems	Operating System 2.09
Battery type	AAA