Special - Maple Help

ComplexBox

 Special
 special functions for ComplexBox objects
 GAMMA
 compute the GAMMA function of a ComplexBox object
 lnGAMMA
 compute the log-GAMMA function of a ComplexBox object
 rGAMMA
 compute the reciprocal GAMMA function of a ComplexBox object
 Psi
 compute the digamma function of a ComplexBox object
 Zeta
 compute the Riemann zeta function of a ComplexBox object
 Ei
 compute the exponential integral of a ComplexBox object
 Si
 compute the sine integral of a ComplexBox object
 Ci
 compute the cosine integral of a ComplexBox object
 Shi
 compute the hyperbolic sine integral of a ComplexBox object
 Chi
 compute the hyperbolic cosine integral of a ComplexBox object
 Li
 compute the logarithmic integral of a ComplexBox object
 dilog
 compute the dilogarithm of a ComplexBox object
 BesselI
 compute the Bessel I function of a ComplexBox object
 BesselJ
 compute the Bessel J function of a ComplexBox object
 BesselK
 compute the Bessel K function of a ComplexBox object
 BesselY
 compute the Bessel Y function of a ComplexBox object
 HermiteH
 compute the Hermite H function of a ComplexBox object
 ChebyshevT
 compute the Chebysheve T function of a ComplexBox object
 ChebyshevU
 compute the Chebysheve U function of a ComplexBox object

 Calling Sequence GAMMA( b ) lnGAMMA( b ) rGAMMA( b ) Psi( b ) Zeta( b ) Ei( b ) Si( b ) Ci( b ) Shi( b ) Chi( b ) Li( b ) dilog( b ) BesselI( a, b ) BesselJ( a, b ) BesselK( a, b ) BesselY( a, b ) HermiteH( a, b ) ChebyshevT( a, b ) ChebyshevU( a, b )

Parameters

 a - ComplexBox object b - ComplexBox object precopt - (optional) equation of the form precision = n, where n is a positive integer

Description

 • The following special functions are defined as methods for ComplexBox objects.

 GAMMA lnGAMMA rGAMMA Psi Zeta dilog Ei Si Ci Li Shi Chi BesselI BesselJ BesselK BesselY HermiteH ChebyshevT ChebyshevU

 • They override the standard Maple procedures for ComplexBox objects.
 • Use the 'precision' = n option to control the precision used in these methods. For more details on precision, see BoxPrecision.

Examples

 > $a≔\mathrm{ComplexBox}\left(1.1+0.0042I\right)$
 ${a}{≔}{⟨}{\text{ComplexBox:}}{\text{[1.1 +/- 1.16415e-10]}}{+}{\text{[0.0042 +/- 4.54747e-13]}}{\cdot }{I}{⟩}$ (1)
 > $b≔\mathrm{ComplexBox}\left(0.234+1.1I\right)$
 ${b}{≔}{⟨}{\text{ComplexBox:}}{\text{[0.234 +/- 1.45519e-11]}}{+}{\text{[1.1 +/- 1.16415e-10]}}{\cdot }{I}{⟩}$ (2)
 > $\mathrm{GAMMA}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.0713942 +/- 1.07348e-09]}}{+}{\text{[-0.431724 +/- 1.09114e-09]}}{\cdot }{I}{⟩}$ (3)
 > $\mathrm{lnGAMMA}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[-0.826479 +/- 1.28212e-09]}}{+}{\text{[-1.40691 +/- 9.81195e-10]}}{\cdot }{I}{⟩}$ (4)
 > $\mathrm{rGAMMA}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.372849 +/- 4.17794e-09]}}{+}{\text{[2.25464 +/- 4.38801e-09]}}{\cdot }{I}{⟩}$ (5)
 > $\mathrm{Ψ}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.0873849 +/- 5.51771e-09]}}{+}{\text{[1.82895 +/- 5.60937e-09]}}{\cdot }{I}{⟩}$ (6)
 > $\mathrm{Zeta}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.0970995 +/- 2.56566e-09]}}{+}{\text{[-0.523928 +/- 2.36614e-09]}}{\cdot }{I}{⟩}$ (7)

Note that arblib uses a different definitino for dilog; this has been corrected for in the external code.

 > $\mathrm{dilog}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.360989 +/- 4.07208e-10]}}{+}{\text{[-1.37139 +/- 3.75221e-10]}}{\cdot }{I}{⟩}$ (8)
 > $\mathrm{Ei}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.606897 +/- 8.20042e-10]}}{+}{\text{[2.51553 +/- 1.41704e-09]}}{\cdot }{I}{⟩}$ (9)
 > $\mathrm{Si}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.283141 +/- 2.45357e-10]}}{+}{\text{[1.16541 +/- 1.05364e-09]}}{\cdot }{I}{⟩}$ (10)
 > $\mathrm{Ci}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.994751 +/- 5.97924e-10]}}{+}{\text{[1.21965 +/- 3.24355e-10]}}{\cdot }{I}{⟩}$ (11)
 > $\mathrm{Li}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.546841 +/- 1.03681e-09]}}{+}{\text{[2.78435 +/- 1.94495e-09]}}{\cdot }{I}{⟩}$ (12)
 > $\mathrm{Shi}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.190056 +/- 1.46752e-10]}}{+}{\text{[1.03758 +/- 6.54464e-10]}}{\cdot }{I}{⟩}$ (13)
 > $\mathrm{Chi}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.416841 +/- 4.15087e-10]}}{+}{\text{[1.47794 +/- 2.68439e-10]}}{\cdot }{I}{⟩}$ (14)
 > $\mathrm{BesselI}\left(a,b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.00590493 +/- 4.76765e-10]}}{+}{\text{[0.438495 +/- 1.71856e-09]}}{\cdot }{I}{⟩}$ (15)
 > $\mathrm{BesselJ}\left(a,b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.0788022 +/- 6.30557e-10]}}{+}{\text{[0.571894 +/- 2.38251e-09]}}{\cdot }{I}{⟩}$ (16)
 > $\mathrm{BesselK}\left(a,b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[-0.553572 +/- 1.18212e-08]}}{+}{\text{[-0.972958 +/- 2.68672e-08]}}{\cdot }{I}{⟩}$ (17)
 > $\mathrm{BesselY}\left(a,b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[-0.651446 +/- 1.15714e-08]}}{+}{\text{[0.412322 +/- 1.91601e-08]}}{\cdot }{I}{⟩}$ (18)
 > $\mathrm{HermiteH}\left(a,b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.138787 +/- 2.82919e-09]}}{+}{\text{[2.46831 +/- 7.96179e-09]}}{\cdot }{I}{⟩}$ (19)
 > $\mathrm{ChebyshevT}\left(a,b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.0185476 +/- 1.66058e-09]}}{+}{\text{[1.25304 +/- 2.96698e-09]}}{\cdot }{I}{⟩}$ (20)
 > $\mathrm{ChebyshevU}\left(a,b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.141167 +/- 8.53773e-09]}}{+}{\text{[2.45801 +/- 1.25366e-08]}}{\cdot }{I}{⟩}$ (21)

Compatibility

 • The ComplexBox[Special], ComplexBox:-GAMMA, ComplexBox:-lnGAMMA, ComplexBox:-rGAMMA, ComplexBox:-Psi, ComplexBox:-Zeta, ComplexBox:-Ei, ComplexBox:-Si, ComplexBox:-Ci, ComplexBox:-Shi, ComplexBox:-Chi, ComplexBox:-Li, ComplexBox:-dilog, ComplexBox:-BesselI, ComplexBox:-BesselJ, ComplexBox:-BesselK, ComplexBox:-BesselY, ComplexBox:-HermiteH, ComplexBox:-ChebyshevT and ComplexBox:-ChebyshevU commands were introduced in Maple 2022.