Hypergeom - Maple Help

RealBox

 Hypergeom
 hypergeometric functions for RealBox objects
 hypergeom
 compute the hypergeometric function of a RealBox object
 CoulombF
 compute the Coulomb F function of a RealBox object
 CoulombG
 compute the Coulomb G function of a RealBox object
 HermiteH
 compute the Hermite H function of a RealBox object
 ChebyshevT
 compute the Chebyshev T function of a RealBox object
 ChebyshevU
 compute the Chebyshev U function of a RealBox object
 JacobiP
 compute the Jacobi P function of a RealBox object
 GegenbauerP
 compute the Gegenbauer C function of a RealBox object
 LaguerreL
 compute the Laguerre L function of a RealBox object
 LegendreP
 compute the Legendre P function of a RealBox object
 KummerU
 compute the Kummer U function of a RealBox object
 KummerM
 compute the Kummer M function of a RealBox object

 Calling Sequence hypergeom( aL, bL, c ) ChebyshevT( a, b ) ChebyshevU( a, b ) CoulombF( a, b, c ) CoulombG( a, b, c ) HermiteH( a, b ) JacobiP( n, a, b, c ) KummerU( a, b, c ) KummerM( a, b, c ) GegenbauerC( n, a, b ) LaguerreL( a, b, c ) LegendreP( a, b ) LegendreP( a, b, c )

Parameters

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

Description

 • A number of hypergeometric functions are defined for RealBox objects:

 CoulombF CoulombG HermiteH ChebyshevT ChebyshevU JacobiP GegenbauerC LaguerreL LegendreP KummerU KummerM hypergeom

 • They override the standard Maple procedures for RealBox 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

 > $\mathrm{hypergeom}\left(\left[\right],\left[\mathrm{RealBox}\left(2\right)\right],\mathrm{RealBox}\left(2.3\right)\right)$
 ${⟨}{\text{RealBox:}}{2.68583}{±}{1.856ⅇ-09}{⟩}$ (1)
 > $a≔\mathrm{RealBox}\left(1.1\right)$
 ${a}{≔}{⟨}{\text{RealBox:}}{1.1}{±}{1.16415ⅇ-10}{⟩}$ (2)
 > $b≔\mathrm{RealBox}\left(2.3\right)$
 ${b}{≔}{⟨}{\text{RealBox:}}{2.3}{±}{2.32831ⅇ-10}{⟩}$ (3)
 > $c≔\mathrm{RealBox}\left(-7.654\right)$
 ${c}{≔}{⟨}{\text{RealBox:}}{-7.654}{±}{4.65661ⅇ-10}{⟩}$ (4)
 > $n≔\mathrm{RealBox}\left(5\right)$
 ${n}{≔}{⟨}{\text{RealBox:}}{5}{±}{0}{⟩}$ (5)
 > $t≔\mathrm{RealBox}\left(2.0\right)$
 ${t}{≔}{⟨}{\text{RealBox:}}{2}{±}{0}{⟩}$ (6)
 > $\mathrm{hypergeom}\left(\left[1,2\right],\left[3,4\right],b\right)$
 ${⟨}{\text{RealBox:}}{1.57075}{±}{1.41963ⅇ-09}{⟩}$ (7)
 > $\mathrm{CoulombF}\left(\mathrm{RealBox}\left(0\right),\mathrm{RealBox}\left(0\right),\mathrm{RealBox}\left(\mathrm{Pi}\right)\right)$
 ${⟨}{\text{RealBox:}}{-1.06352ⅇ-10}{±}{1.00863ⅇ-08}{⟩}$ (8)
 > $\mathrm{CoulombG}\left(n,a,b\right)$
 ${⟨}{\text{RealBox:}}{74.681}{±}{1.50885ⅇ-06}{⟩}$ (9)
 > $\mathrm{ChebyshevT}\left(a,b\right)$
 ${⟨}{\text{RealBox:}}{2.63169}{±}{2.3599ⅇ-09}{⟩}$ (10)
 > $\mathrm{ChebyshevU}\left(a,b\right)$
 ${⟨}{\text{RealBox:}}{5.33486}{±}{1.14856ⅇ-08}{⟩}$ (11)
 > $\mathrm{GegenbauerC}\left(n,a,b\right)$
 ${⟨}{\text{RealBox:}}{2110.19}{±}{6.35073ⅇ-06}{⟩}$ (12)
 > $\mathrm{JacobiP}\left(n,a,b,c\right)$
 ${⟨}{\text{RealBox:}}{-1.32471ⅇ+06}{±}{0.0128264}{⟩}$ (13)
 > $\mathrm{KummerU}\left(a,c,b\right)$
 ${⟨}{\text{RealBox:}}{0.0698887}{±}{1.51965ⅇ-08}{⟩}$ (14)
 > $\mathrm{KummerM}\left(a,c,b\right)$
 ${⟨}{\text{RealBox:}}{4.06526}{±}{7.20886ⅇ-08}{⟩}$ (15)
 > $\mathrm{LaguerreL}\left(n,a,b\right)$
 ${⟨}{\text{RealBox:}}{0.288414}{±}{1.21033ⅇ-07}{⟩}$ (16)
 > $\mathrm{LegendreP}\left(a,b\right)$
 ${⟨}{\text{RealBox:}}{2.56247}{±}{3.65995ⅇ-09}{⟩}$ (17)
 > $\mathrm{LegendreP}\left(n,a,b\right)$
 ${⟨}{\text{RealBox:}}{2314.71}{±}{1.40768ⅇ-05}{⟩}$ (18)

Compatibility

 • The RealBox[Hypergeom], RealBox:-hypergeom, RealBox:-CoulombF, RealBox:-CoulombG, RealBox:-HermiteH, RealBox:-ChebyshevT, RealBox:-ChebyshevU, RealBox:-JacobiP, RealBox:-GegenbauerP, RealBox:-LaguerreL, RealBox:-LegendreP, RealBox:-KummerU and RealBox:-KummerM commands were introduced in Maple 2022.