Incomplete Gamma and Related Functions - 8.15 Sums

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
8.15.E1	${\displaystyle{\displaystyle\gamma\left(a,\lambda x\right)=\lambda^{a}\sum_{k=0}^{\infty}\gamma\left(a+k,x\right)\frac{(1-\lambda)^{k}}{k!}}}$ \incgamma@{a}{\lambda x} = \lambda^{a}\sum_{k=0}^{\infty}\incgamma@{a+k}{x}\frac{(1-\lambda)^{k}}{k!}	${\displaystyle{\displaystyle\Re a>0,\Re(a+k)>0}}$	GAMMA(a)-GAMMA(a, lambda*x) = (lambda)^(a)* sum(GAMMA(a + k)-GAMMA(a + k, x)*((1 - lambda)^(k))/(factorial(k)), k = 0..infinity)	Gamma[a, 0, \[Lambda]*x] == \[Lambda]^(a)* Sum[Gamma[a + k, 0, x]*Divide[(1 - \[Lambda])^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Failed [90 / 90] Result: Float(infinity)+Float(infinity)*I Test Values: {a = 1.5, lambda = 1/2*3^(1/2)+1/2*I, x = 1.5} Result: Float(infinity)+Float(infinity)*I Test Values: {a = 1.5, lambda = 1/2*3^(1/2)+1/2*I, x = .5} ... skip entries to safe data	Skipped - Because timed out