Functions of Number Theory - 27.13 Functions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
27.13.E4	${\displaystyle{\displaystyle\vartheta\left(x\right)=1+2\sum_{m=1}^{\infty}x^{m^{2}}}}$ \AThetaFunction@{x} = 1+2\sum_{m=1}^{\infty}x^{m^{2}}	${\displaystyle{\displaystyle|x|<1}}$	1+2*(sum((x)^(m^2), m = 1 .. infinity)) = 1 + 2*sum((x)^((m)^(2)), m = 1..infinity)	Error	Successful	Missing Macro Error	-	-
27.13.E6	${\displaystyle{\displaystyle(\vartheta\left(x\right))^{2}=1+4\sum_{n=1}^{\infty}\left(\delta_{1}(n)-\delta_{3}(n)\right)x^{n}}}$ (\AThetaFunction@{x})^{2} = 1+4\sum_{n=1}^{\infty}\left(\delta_{1}(n)-\delta_{3}(n)\right)x^{n}	${\displaystyle{\displaystyle|x|<1}}$	(1+2*(sum((x)^(m^2), m = 1 .. infinity)))^(2) = 1 + 4*sum((delta[1](n)- delta[3](n))*(x)^(n), n = 1..infinity)	Error	Failure	Missing Macro Error	Failed [300 / 300] Result: 3.532372013 Test Values: {delta = 1/2*3^(1/2)+1/2*I, x = 1/2, delta[1] = 1/2*3^(1/2)+1/2*I, delta[3] = 1/2*3^(1/2)+1/2*I} Result: -7.395831219+2.928203232*I Test Values: {delta = 1/2*3^(1/2)+1/2*I, x = 1/2, delta[1] = 1/2*3^(1/2)+1/2*I, delta[3] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	-