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ComplexBox

 Hypergeom
 hypergeometric functions for ComplexBox objects
 hypergeom
 compute the hypergeometric function of a ComplexBox object
 KummerU
 compute the Kummer U function of a ComplexBox object
 LegendreP
 compute the Legendre P function of a ComplexBox object
 LegendreQ
 compute the Legendre Q function of a ComplexBox object

 Calling Sequence hypergeom( aL, bL, c ) KummerU( a, b, c ) LegendreP( a, b ) LegendreP( a, b, c ) LegendreQ( a, b ) LegendreQ( a, b, c )

Parameters

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

Description

 • Several hypergeometric functions are defined for ComplexBox objects:

 LegendreP LegendreQ KummerU hypergeom

 • 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.

Examples

 > $\mathrm{hypergeom}\left(\left[\right],\left[\mathrm{ComplexBox}\left(2\right)\right],\mathrm{ComplexBox}\left(2.3\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[2.68583 +/- 1.856e-09]}}{+}{\text{[0 +/- 0]}}{\cdot }{I}{⟩}$ (1)
 > $a≔\mathrm{ComplexBox}\left(I-1.1\right)$
 ${a}{≔}{⟨}{\text{ComplexBox:}}{\text{[-1.1 +/- 1.16415e-10]}}{+}{\text{[1 +/- 0]}}{\cdot }{I}{⟩}$ (2)
 > $b≔\mathrm{ComplexBox}\left(2.3+4.7I\right)$
 ${b}{≔}{⟨}{\text{ComplexBox:}}{\text{[2.3 +/- 2.32831e-10]}}{+}{\text{[4.7 +/- 4.65661e-10]}}{\cdot }{I}{⟩}$ (3)
 > $c≔\mathrm{ComplexBox}\left(0.423I\right)$
 ${c}{≔}{⟨}{\text{ComplexBox:}}{\text{[0 +/- 0]}}{+}{\text{[0.423 +/- 2.91038e-11]}}{\cdot }{I}{⟩}$ (4)
 > $n≔\mathrm{ComplexBox}\left(5\right)$
 ${n}{≔}{⟨}{\text{ComplexBox:}}{\text{[5 +/- 0]}}{+}{\text{[0 +/- 0]}}{\cdot }{I}{⟩}$ (5)
 > $t≔\mathrm{ComplexBox}\left(2.0+I\right)$
 ${t}{≔}{⟨}{\text{ComplexBox:}}{\text{[2 +/- 0]}}{+}{\text{[1 +/- 0]}}{\cdot }{I}{⟩}$ (6)
 > $\mathrm{hypergeom}\left(\left[1,2\right],\left[3,4\right],b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.609955 +/- 2.15311e-09]}}{+}{\text{[0.905206 +/- 2.53906e-09]}}{\cdot }{I}{⟩}$ (7)
 > $\mathrm{KummerU}\left(a,c,b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[19.6016 +/- 9.82046e-07]}}{+}{\text{[-9.57351 +/- 9.80962e-07]}}{\cdot }{I}{⟩}$ (8)
 > $\mathrm{LegendreP}\left(a,b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[-0.135347 +/- 1.31999e-07]}}{+}{\text{[-2.14748 +/- 1.32695e-07]}}{\cdot }{I}{⟩}$ (9)
 > $\mathrm{LegendreP}\left(n,a,b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[1643.53 +/- 0.000122696]}}{+}{\text{[4439.07 +/- 0.000124512]}}{\cdot }{I}{⟩}$ (10)
 > $\mathrm{LegendreQ}\left(\mathrm{ComplexBox}\left(2\right),\mathrm{ComplexBox}\left(I-1.1\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.0335524 +/- 3.42359e-10]}}{+}{\text{[-0.020433 +/- 3.44947e-10]}}{\cdot }{I}{⟩}$ (11)

Compatibility

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