Confluent Hypergeometric Functions - 13.31 Approximations

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
13.31.E3	${\displaystyle{\displaystyle z^{a}U\left(a,1+a-b,z\right)=\lim_{n\to\infty}\frac{A_{n}(z)}{B_{n}(z)}}}$ z^{a}\KummerconfhyperU@{a}{1+a-b}{z} = \lim_{n\to\infty}\frac{A_{n}(z)}{B_{n}(z)}		(z)^(a)* KummerU(a, 1 + a - b, z) = limit((sum((pochhammer(- n, s)*pochhammer(n + 1, s)*pochhammer(a, s)*pochhammer(b, s))/(pochhammer(a + 1, s)*pochhammer(b + 1, s)*(factorial(n))^(2))* hypergeom([- n + s , n + 1 + s , 1], [1 + s , a + 1 + s , b + 1 + s], - z), s = 0..n))/(hypergeom([- n , n + 1], [a + 1 , b + 1], - z)), n = infinity)	(z)^(a)* HypergeometricU[a, 1 + a - b, z] == Limit[Divide[Sum[Divide[Pochhammer[- n, s]*Pochhammer[n + 1, s]*Pochhammer[a, s]*Pochhammer[b, s],Pochhammer[a + 1, s]*Pochhammer[b + 1, s]*((n)!)^(2)]* HypergeometricPFQ[{- n + s , n + 1 + s , 1}, {1 + s , a + 1 + s , b + 1 + s}, - z], {s, 0, n}, GenerateConditions->None],HypergeometricPFQ[{- n , n + 1}, {a + 1 , b + 1}, - z]], n -> Infinity, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out