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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 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

 > $a≔\mathrm{RealBox}\left(1.1\right)$
 ${a}{≔}{⟨}{\text{RealBox:}}{1.1}{±}{1.16415ⅇ-10}{⟩}$ (1)
 > $b≔\mathrm{RealBox}\left(-2.3\right)$
 ${b}{≔}{⟨}{\text{RealBox:}}{-2.3}{±}{2.32831ⅇ-10}{⟩}$ (2)
 > $\mathrm{GAMMA}\left(b\right)$
 ${⟨}{\text{RealBox:}}{-1.44711}{±}{4.69909ⅇ-09}{⟩}$ (3)

This should be (approximately) $\sqrt{\mathrm{\pi }}$.

 > $\mathrm{GAMMA}\left(\mathrm{RealBox}\left(0.5\right)\right)$
 ${⟨}{\text{RealBox:}}{1.77245}{±}{1.16415ⅇ-10}{⟩}$ (4)
 > $\mathrm{lnGAMMA}\left(a\right)$
 ${⟨}{\text{RealBox:}}{-0.0498724}{±}{9.63431ⅇ-10}{⟩}$ (5)
 > $\mathrm{rGAMMA}\left(b\right)$
 ${⟨}{\text{RealBox:}}{-0.691034}{±}{2.22252ⅇ-09}{⟩}$ (6)
 > $\mathrm{Zeta}\left(b\right)$
 ${⟨}{\text{RealBox:}}{0.00651938}{±}{1.7552ⅇ-11}{⟩}$ (7)
 > $\mathrm{HurwitzZeta}\left(b,a\right)$
 ${⟨}{\text{RealBox:}}{-0.0082905}{±}{4.98256ⅇ-07}{⟩}$ (8)
 > $\mathrm{Ψ}\left(b\right)$
 ${⟨}{\text{RealBox:}}{3.31732}{±}{1.1879ⅇ-08}{⟩}$ (9)
 > $\mathrm{dilog}\left(a\right)$
 ${⟨}{\text{RealBox:}}{-0.0976052}{±}{1.30136ⅇ-10}{⟩}$ (10)
 > $\mathrm{erf}\left(b\right)$
 ${⟨}{\text{RealBox:}}{-0.998857}{±}{1.42847ⅇ-10}{⟩}$ (11)
 > $\mathrm{erfc}\left(b\right)$
 ${⟨}{\text{RealBox:}}{1.99886}{±}{2.59262ⅇ-10}{⟩}$ (12)
 > $\mathrm{erfi}\left(b\right)$
 ${⟨}{\text{RealBox:}}{-55.7397}{±}{6.03707ⅇ-08}{⟩}$ (13)
 > $\mathrm{BesselI}\left(b,a\right)$
 ${⟨}{\text{RealBox:}}{1.07222}{±}{1.06615ⅇ-08}{⟩}$ (14)
 > $\mathrm{BesselJ}\left(b,a\right)$
 ${⟨}{\text{RealBox:}}{1.58505}{±}{1.53202ⅇ-08}{⟩}$ (15)
 > $\mathrm{BesselK}\left(b,a\right)$
 ${⟨}{\text{RealBox:}}{1.88153}{±}{2.40801ⅇ-08}{⟩}$ (16)
 > $\mathrm{BesselY}\left(b,a\right)$
 ${⟨}{\text{RealBox:}}{-1.04545}{±}{1.37516ⅇ-08}{⟩}$ (17)
 > $\mathrm{Li}\left(a\right)$
 ${⟨}{\text{RealBox:}}{-1.67577}{±}{1.7292ⅇ-09}{⟩}$ (18)
 > $\mathrm{Ei}\left(b\right)$
 ${⟨}{\text{RealBox:}}{-0.0325023}{±}{2.50101ⅇ-09}{⟩}$ (19)
 > $\mathrm{Si}\left(b\right)$
 ${⟨}{\text{RealBox:}}{-1.72221}{±}{1.93419ⅇ-09}{⟩}$ (20)
 > $\mathrm{Ci}\left(a\right)$
 ${⟨}{\text{RealBox:}}{0.384873}{±}{4.0223ⅇ-10}{⟩}$ (21)
 > $\mathrm{Shi}\left(b\right)$
 ${⟨}{\text{RealBox:}}{-3.09344}{±}{3.68307ⅇ-09}{⟩}$ (22)
 > $\mathrm{Chi}\left(a\right)$
 ${⟨}{\text{RealBox:}}{0.990694}{±}{5.7548ⅇ-10}{⟩}$ (23)
 > $\mathrm{AiryAi}\left(b\right)$
 ${⟨}{\text{RealBox:}}{0.0267063}{±}{1.69826ⅇ-10}{⟩}$ (24)
 > $\mathrm{AiryAi}\left(1,b\right)$
 ${⟨}{\text{RealBox:}}{0.700034}{±}{3.13003ⅇ-10}{⟩}$ (25)
 > $\mathrm{AiryBi}\left(b\right)$
 ${⟨}{\text{RealBox:}}{-0.454928}{±}{1.97113ⅇ-10}{⟩}$ (26)
 > $\mathrm{AiryBi}\left(1,b\right)$
 ${⟨}{\text{RealBox:}}{-0.00581106}{±}{2.55252ⅇ-10}{⟩}$ (27)
 > $\mathrm{AiryAi}\left(3,b\right)$
 ${⟨}{\text{RealBox:}}{-1.58337}{±}{1.28555ⅇ-09}{⟩}$ (28)
 > $\mathrm{AiryBi}\left(3,b\right)$
 ${⟨}{\text{RealBox:}}{-0.441563}{±}{8.15559ⅇ-10}{⟩}$ (29)
 > $\mathrm{LambertW}\left(a\right)$
 ${⟨}{\text{RealBox:}}{0.602304}{±}{1.13646ⅇ-10}{⟩}$ (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.