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

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.

$a≔\mathrm{ComplexBox}\left(1.1+0.0042\mathrm{I}\right)$

$a≔⟨\text{ComplexBox:}\text{[1.1 +/- 1.16415e-10]}+\text{[0.0042 +/- 4.54747e-13]}\cdot \mathrm{I}⟩$

$b≔\mathrm{ComplexBox}\left(0.234+1.1\mathrm{I}\right)$

$b≔⟨\text{ComplexBox:}\text{[0.234 +/- 1.45519e-11]}+\text{[1.1 +/- 1.16415e-10]}\cdot \mathrm{I}⟩$

$\mathrm{\Gamma }\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.0713942 +/- 1.07348e-09]}+\text{[-0.431724 +/- 1.09114e-09]}\cdot \mathrm{I}⟩$

$\mathrm{lnGAMMA}\left(b\right)$

$⟨\text{ComplexBox:}\text{[-0.826479 +/- 1.28212e-09]}+\text{[-1.40691 +/- 9.81195e-10]}\cdot \mathrm{I}⟩$

$\mathrm{rGAMMA}\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.372849 +/- 4.17794e-09]}+\text{[2.25464 +/- 4.38801e-09]}\cdot \mathrm{I}⟩$

$\mathrm{\Psi }\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.0873849 +/- 5.51771e-09]}+\text{[1.82895 +/- 5.60937e-09]}\cdot \mathrm{I}⟩$

$\mathrm{\zeta }\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.0970995 +/- 2.56566e-09]}+\text{[-0.523928 +/- 2.36614e-09]}\cdot \mathrm{I}⟩$

$\mathrm{dilog}\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.360989 +/- 4.07208e-10]}+\text{[-1.37139 +/- 3.75221e-10]}\cdot \mathrm{I}⟩$

$\mathrm{Ei}\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.606897 +/- 8.20042e-10]}+\text{[2.51553 +/- 1.41704e-09]}\cdot \mathrm{I}⟩$

$\mathrm{Si}\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.283141 +/- 2.45357e-10]}+\text{[1.16541 +/- 1.05364e-09]}\cdot \mathrm{I}⟩$

$\mathrm{Ci}\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.994751 +/- 5.97924e-10]}+\text{[1.21965 +/- 3.24355e-10]}\cdot \mathrm{I}⟩$

$\mathrm{Li}\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.546841 +/- 1.03681e-09]}+\text{[2.78435 +/- 1.94495e-09]}\cdot \mathrm{I}⟩$

$\mathrm{Shi}\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.190056 +/- 1.46752e-10]}+\text{[1.03758 +/- 6.54464e-10]}\cdot \mathrm{I}⟩$

$\mathrm{Chi}\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.416841 +/- 4.15087e-10]}+\text{[1.47794 +/- 2.68439e-10]}\cdot \mathrm{I}⟩$

$\mathrm{BesselI}\left(a\,b\right)$

$⟨\text{ComplexBox:}\text{[0.00590493 +/- 4.76765e-10]}+\text{[0.438495 +/- 1.71856e-09]}\cdot \mathrm{I}⟩$

$\mathrm{BesselJ}\left(a\,b\right)$

$⟨\text{ComplexBox:}\text{[0.0788022 +/- 6.30557e-10]}+\text{[0.571894 +/- 2.38251e-09]}\cdot \mathrm{I}⟩$

$\mathrm{BesselK}\left(a\,b\right)$

$⟨\text{ComplexBox:}\text{[-0.553572 +/- 1.18212e-08]}+\text{[-0.972958 +/- 2.68672e-08]}\cdot \mathrm{I}⟩$

$\mathrm{BesselY}\left(a\,b\right)$

$⟨\text{ComplexBox:}\text{[-0.651446 +/- 1.15714e-08]}+\text{[0.412322 +/- 1.91601e-08]}\cdot \mathrm{I}⟩$

$\mathrm{HermiteH}\left(a\,b\right)$

$⟨\text{ComplexBox:}\text{[0.138787 +/- 2.82919e-09]}+\text{[2.46831 +/- 7.96179e-09]}\cdot \mathrm{I}⟩$

$\mathrm{ChebyshevT}\left(a\,b\right)$

$⟨\text{ComplexBox:}\text{[0.0185476 +/- 1.66058e-09]}+\text{[1.25304 +/- 2.96698e-09]}\cdot \mathrm{I}⟩$

$\mathrm{ChebyshevU}\left(a\,b\right)$

$⟨\text{ComplexBox:}\text{[0.141167 +/- 8.53773e-09]}+\text{[2.45801 +/- 1.25366e-08]}\cdot \mathrm{I}⟩$

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.

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