Several hypergeometric functions are defined for ComplexBox objects:

They override the standard Maple procedures for ComplexBox objects, or certain special cases of the Maple hypergeom procedure.

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

$\mathrm{hypergeom}\left(\left[\right]\,\left[\mathrm{ComplexBox}\left(2\right)\right]\,\mathrm{ComplexBox}\left(2.3\right)\right)$

$⟨\text{ComplexBox:}\text{[2.68583 +/- 1.856e-09]}+\text{[0 +/- 0]}\cdot \mathrm{I}⟩$

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

$a≔⟨\text{ComplexBox:}\text{[-1.1 +/- 1.16415e-10]}+\text{[1 +/- 0]}\cdot \mathrm{I}⟩$

$b≔\mathrm{ComplexBox}\left(2.3+4.7\mathrm{I}\right)$

$b≔⟨\text{ComplexBox:}\text{[2.3 +/- 2.32831e-10]}+\text{[4.7 +/- 4.65661e-10]}\cdot \mathrm{I}⟩$

$c≔\mathrm{ComplexBox}\left(0.423\mathrm{I}\right)$

$c≔⟨\text{ComplexBox:}\text{[0 +/- 0]}+\text{[0.423 +/- 2.91038e-11]}\cdot \mathrm{I}⟩$

$n≔\mathrm{ComplexBox}\left(5\right)$

$n≔⟨\text{ComplexBox:}\text{[5 +/- 0]}+\text{[0 +/- 0]}\cdot \mathrm{I}⟩$

$t≔\mathrm{ComplexBox}\left(2.0+\mathrm{I}\right)$

$t≔⟨\text{ComplexBox:}\text{[2 +/- 0]}+\text{[1 +/- 0]}\cdot \mathrm{I}⟩$

$\mathrm{hypergeom}\left(\left[1\,2\right]\,\left[3\,4\right]\,b\right)$

$⟨\text{ComplexBox:}\text{[0.609955 +/- 2.15311e-09]}+\text{[0.905206 +/- 2.53906e-09]}\cdot \mathrm{I}⟩$

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

$⟨\text{ComplexBox:}\text{[19.6016 +/- 9.82046e-07]}+\text{[-9.57351 +/- 9.80962e-07]}\cdot \mathrm{I}⟩$

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

$⟨\text{ComplexBox:}\text{[-0.135347 +/- 1.31999e-07]}+\text{[-2.14748 +/- 1.32695e-07]}\cdot \mathrm{I}⟩$

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

$⟨\text{ComplexBox:}\text{[1643.53 +/- 0.000122696]}+\text{[4439.07 +/- 0.000124512]}\cdot \mathrm{I}⟩$

$\mathrm{LegendreQ}\left(\mathrm{ComplexBox}\left(2\right)\,\mathrm{ComplexBox}\left(\mathrm{I}-1.1\right)\right)$

$⟨\text{ComplexBox:}\text{[0.0335524 +/- 3.42359e-10]}+\text{[-0.020433 +/- 3.44947e-10]}\cdot \mathrm{I}⟩$

The ComplexBox[Hypergeom], ComplexBox:-hypergeom, ComplexBox:-KummerU, ComplexBox:-LegendreP and ComplexBox:-LegendreQ commands were introduced in Maple 2022.

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