The Error Function - Maple Help

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erf - The Error Function

erfc - The Complementary Error Function and its Iterated Integrals

erfi - The Imaginary Error Function

Calling Sequence

erf(x)

erfc(x)

erfc(n, x)

erfi(x)

Parameters

x

-

algebraic expression

n

-

algebraic expression, understood to be an integer  1

Description

• 

The error function is defined for all complex x by

erfx=20xⅇt2ⅆtπ

• 

The complementary error function is defined by

erfcx=1erfx=12π120xⅇt2ⅆt

• 

The iterated integrals of the complementary error function are defined by

erfc1,x=2πⅇx2

erfcn,x=xerfcn1,tⅆtn0

  

(Note erfc0,x=erfcx.)

• 

The imaginary error function is defined by

erfix=IerfIx=2π0xⅇt2ⅆt

• 

All of these functions are entire.

Examples

erf∞

1

(1)

erf3

erf3

(2)

evalf

0.9999779095

(3)

erfc3.

0.00002209049700

(4)

erf1.1.I

1.3161512820.1904534692I

(5)

erfc1.52.85I

62.8206488910.56167495I

(6)

ⅆⅆxerfx

2ⅇx2π

(7)

ⅆⅆxerfc5,x

erfc4,x

(8)

erfix

erfix

(9)

serieserfix,x,4

2πx+23πx3+Ox4

(10)

expanderfc2,x,x

12x212x2erfx12xⅇx2π+1414erfx

(11)

convert,erfc

12x212x21erfcx12xⅇx2π+14erfcx

(12)

See Also

convert, dawson, Fresnel, initialfunctions

References

  

Erdelyi, A. Higher Transcendental Functions. McGraw-Hill, 1953. Vol. 2.


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