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RealBox

  

Special

  

special functions for RealBox objects

  

GAMMA

  

compute the gamma function of a RealBox object

  

lnGAMMA

  

compute the lnGamma function of a RealBox object

  

rGAMMA

  

compute the reciprocal GAMMA function of a RealBox object

  

Zeta

  

compute the Zeta function of a RealBox object

  

Psi

  

compute the Psi function of a RealBox object

  

dilog

  

compute the dilog function of a RealBox object

  

erf

  

compute the error function of a RealBox object

  

erfc

  

compute the complementary error function of a RealBox object

  

erfi

  

compute the imaginary error function of a RealBox object

  

BesselI

  

compute the Besel I function of a RealBox object

  

BesselJ

  

compute the Besel J function of a RealBox object

  

BesselK

  

compute the Besel K function of a RealBox object

  

BesselY

  

compute the Besel Y function of a RealBox object

  

Ei

  

compute the exponential integral function of a RealBox object

  

Si

  

compute the sine integral function of a RealBox object

  

Ci

  

compute the cosine integral function of a RealBox object

  

Shi

  

compute the hyperbolic sine integral function of a RealBox object

  

Chi

  

compute the hyperbolic cosine integral function of a RealBox object

  

AiryAi

  

compute the Airy Ai wave function of a RealBox object

  

AiryBi

  

compute the Airy Bi wave function of a RealBox object

  

LambertW

  

compute the Lambert W function of a RealBox object

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

GAMMA( b )

lnGAMMA( b )

rGAMMA( b )

Zeta( b )

Psi( b )

dilog( b )

erf( b )

erfc( b )

erfi( b )

BesselI( a, b )

BesselJ( a, b )

BesselK( a, b )

BesselY( a, b )

Ei( b )

Si( b )

Ci( b )

Shi( b )

Chi( b )

AiryAi( b )

AiryAi( 1, b )

AiryBi( b )

AiryBi( 1, b )

LambertW( b )

Parameters

a

-

RealBox object

b

-

RealBox object

precopt

-

(optional) equation of the form precision = n, where n is a positive integer

Description

• 

Many special functions are defined for RealBox objects. The following table briefly describes those that are currently implemented.

GAMMA( b )

GAMMA function

lnGAMMA( b )

lnGAMMA function

rGAMMA( b )

reciprocal GAMMA function

Zeta( b )

Riemann Zeta function

HurwitzZeta( a, b )

Hurwitz Zeta function

Psi( b )

digamma function

dilog( b )

dilogarithm

erf( b )

error function

erfc( b )

error function

erfi( b )

error function

BesselI( a, b )

Bessel I function

BesselJ( a, b )

Bessel J function

BesselK( a, b )

Bessel K function

BesselY( a, b )

Bessel Y function

Li( b )

logarithmic integral

Ei( b )

exponential integral

Si( b )

sine integral

Ci( b )

cosine integral

Shi( b )

hyperbolic sine integral

Chi( b )

hyperbolic cosine integral

AiryAi( b )

Airy Ai function

AiryAi( 1, b )

first derivative of Ai

AiryBi( b )

Airy Bi function

AiryBi( 1, b )

first derivative of Bi

LambertW( b )

Lambert W function

polylog( a, b )

general polylogarithm function

• 

Use the 'precision' = n option to control the precision used in these methods. For more details on precision, see BoxPrecision.

Examples

aRealBox1.1

aRealBox: 1.1±1.16415ⅇ-10

(1)

bRealBox2.3

bRealBox: -2.3±2.32831ⅇ-10

(2)

GAMMAb

RealBox: -1.44711±4.69909ⅇ-09

(3)

This should be (approximately) π.

GAMMARealBox0.5

RealBox: 1.77245±1.16415ⅇ-10

(4)

lnGAMMAa

RealBox: -0.0498724±9.63431ⅇ-10

(5)

rGAMMAb

RealBox: -0.691034±2.22252ⅇ-09

(6)

Zetab

RealBox: 0.00651938±1.7552ⅇ-11

(7)

HurwitzZetab,a

RealBox: -0.0082905±4.98256ⅇ-07

(8)

Ψb

RealBox: 3.31732±1.1879ⅇ-08

(9)

diloga

RealBox: -0.0976052±1.30136ⅇ-10

(10)

erfb

RealBox: -0.998857±1.42847ⅇ-10

(11)

erfcb

RealBox: 1.99886±2.59262ⅇ-10

(12)

erfib

RealBox: -55.7397±6.03707ⅇ-08

(13)

BesselIb,a

RealBox: 1.07222±1.06615ⅇ-08

(14)

BesselJb,a

RealBox: 1.58505±1.53202ⅇ-08

(15)

BesselKb,a

RealBox: 1.88153±2.40801ⅇ-08

(16)

BesselYb,a

RealBox: -1.04545±1.37516ⅇ-08

(17)

Lia

RealBox: -1.67577±1.7292ⅇ-09

(18)

Eib

RealBox: -0.0325023±2.50101ⅇ-09

(19)

Sib

RealBox: -1.72221±1.93419ⅇ-09

(20)

Cia

RealBox: 0.384873±4.0223ⅇ-10

(21)

Shib

RealBox: -3.09344±3.68307ⅇ-09

(22)

Chia

RealBox: 0.990694±5.7548ⅇ-10

(23)

AiryAib

RealBox: 0.0267063±1.69826ⅇ-10

(24)

AiryAi1,b

RealBox: 0.700034±3.13003ⅇ-10

(25)

AiryBib

RealBox: -0.454928±1.97113ⅇ-10

(26)

AiryBi1,b

RealBox: -0.00581106±2.55252ⅇ-10

(27)

AiryAi3,b

RealBox: -1.58337±1.28555ⅇ-09

(28)

AiryBi3,b

RealBox: -0.441563±8.15559ⅇ-10

(29)

LambertWa

RealBox: 0.602304±1.13646ⅇ-10

(30)

Compatibility

• 

The RealBox[Special], RealBox:-GAMMA, RealBox:-lnGAMMA, RealBox:-rGAMMA, RealBox:-Zeta, RealBox:-Psi, RealBox:-dilog, RealBox:-erf, RealBox:-erfc, RealBox:-erfi, RealBox:-BesselI, RealBox:-BesselJ, RealBox:-BesselK, RealBox:-BesselY, RealBox:-Ei, RealBox:-Si, RealBox:-Ci, RealBox:-Shi, RealBox:-Chi, RealBox:-AiryAi, RealBox:-AiryBi and RealBox:-LambertW commands were introduced in Maple 2022.

• 

For more information on Maple 2022 changes, see Updates in Maple 2022.

See Also

ComplexBox

ComplexBox[Circular]

RealBox

RealBox[Circular]

RealBox[Hyperbolic]