Confluent Hypergeometric Functions - 13.7 Asymptotic Expansions for Large Argument

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
13.7.E4	${\displaystyle{\displaystyle U\left(a,b,z\right)=z^{-a}\sum_{s=0}^{n-1}\frac{{\left(a\right)_{s}}{\left(a-b+1\right)_{s}}}{s!}(-z)^{-s}+\varepsilon_{n}(z)}}$ \KummerconfhyperU@{a}{b}{z} = z^{-a}\sum_{s=0}^{n-1}\frac{\Pochhammersym{a}{s}\Pochhammersym{a-b+1}{s}}{s!}(-z)^{-s}+\varepsilon_{n}(z)		KummerU(a, b, z) = (z)^(- a)* sum((pochhammer(a, s)*pochhammer(a - b + 1, s))/(factorial(s))*(- z)^(- s), s = 0..n - 1)+ varepsilon[n](z)	HypergeometricU[a, b, z] == (z)^(- a)* Sum[Divide[Pochhammer[a, s]*Pochhammer[a - b + 1, s],(s)!]*(- z)^(- s), {s, 0, n - 1}, GenerateConditions->None]+ Subscript[\[CurlyEpsilon], n][z]	Failure	Failure	Failed [300 / 300] Result: 1.515657870-.5735934827*I Test Values: {a = -3/2, b = -3/2, z = 1/2*3^(1/2)+1/2*I, varepsilon[n] = 1/2*3^(1/2)+1/2*I, n = 1, varepsilon = 1} Result: 1.515657870-.5735934827*I Test Values: {a = -3/2, b = -3/2, z = 1/2*3^(1/2)+1/2*I, varepsilon[n] = 1/2*3^(1/2)+1/2*I, n = 1, varepsilon = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[1.515657869456145, -0.5735934817267648] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ε, 1], Rule[Subscript[ε, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.515657869456145, -0.5735934817267648] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ε, 2], Rule[Subscript[ε, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.7.E10	${\displaystyle{\displaystyle U\left(a,b,z\right)=z^{-a}\sum_{s=0}^{n-1}\frac{{\left(a\right)_{s}}{\left(a-b+1\right)_{s}}}{s!}(-z)^{-s}+R_{n}(a,b,z)}}$ \KummerconfhyperU@{a}{b}{z} = z^{-a}\sum_{s=0}^{n-1}\frac{\Pochhammersym{a}{s}\Pochhammersym{a-b+1}{s}}{s!}(-z)^{-s}+R_{n}(a,b,z)	${\displaystyle{\displaystyle\Re a>0,\Re(a-b+1)>0}}$	KummerU(a, b, z) = (z)^(- a)* sum((pochhammer(a, s)*pochhammer(a - b + 1, s))/(factorial(s))*(- z)^(- s)+(((- 1)^(n)* 2*Pi*(z)^(a - b))/(GAMMA(a)*GAMMA(a - b + 1))*(sum((pochhammer(1 - a, s)*pochhammer(b - a, s))/(factorial(s))*(- z)^(- s)* G[n + 2*a - b - s](z), s = 0..m - 1)+ pochhammer(1 - a, m)*pochhammer(b - a, m)*R[m , n](a , b , z))), s = 0..n - 1)	HypergeometricU[a, b, z] == (z)^(- a)* Sum[Divide[Pochhammer[a, s]*Pochhammer[a - b + 1, s],(s)!]*(- z)^(- s)+(Divide[(- 1)^(n)* 2*Pi*(z)^(a - b),Gamma[a]*Gamma[a - b + 1]]*(Sum[Divide[Pochhammer[1 - a, s]*Pochhammer[b - a, s],(s)!]*(- z)^(- s)* Subscript[G, n + 2*a - b - s][z], {s, 0, m - 1}, GenerateConditions->None]+ Pochhammer[1 - a, m]*Pochhammer[b - a, m]*Subscript[R, m , n][a , b , z])), {s, 0, n - 1}, GenerateConditions->None]	Failure	Failure	Failed [300 / 300] Result: .1211969897-.2855680854e-1*I+(-.7071067811+.7071067809*I)*(2.023326709-.5908179514*I+(.8862269255-1.534990063*I)*(1.500000000, -1.500000000, .8660254040+.5000000000*I)) Test Values: {a = 3/2, b = -3/2, z = 1/2*3^(1/2)+1/2*I, G[n+2*a-b-s] = 1/2*3^(1/2)+1/2*I, R[m,n] = 1/2*3^(1/2)+1/2*I, m = 1, n = 1} Result: .1211969897-.2855680854e-1*I+(-.7071067811+.7071067809*I)*(-6.242805838+4.181635900*I+(-1.772453851+3.069980127*I)*(1.500000000, -1.500000000, .8660254040+.5000000000*I)) Test Values: {a = 3/2, b = -3/2, z = 1/2*3^(1/2)+1/2*I, G[n+2*a-b-s] = 1/2*3^(1/2)+1/2*I, R[m,n] = 1/2*3^(1/2)+1/2*I, m = 1, n = 2} ... skip entries to safe data	Error