Struve and Related Functions - 11.11 Asymptotic Expansions of Anger–Weber Functions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
11.11#Ex1	${\displaystyle{\displaystyle a_{0}(\lambda)=\frac{1}{1+\lambda}}}$ a_{0}(\lambda) = \frac{1}{1+\lambda}		a[0](lambda) = (1)/(1 + lambda)	Subscript[a, 0][\[Lambda]] == Divide[1,1 + \[Lambda]]	Skipped - no semantic math	Skipped - no semantic math	-	-
11.11#Ex2	${\displaystyle{\displaystyle a_{1}(\lambda)=-\frac{\lambda}{2(1+\lambda)^{4}}}}$ a_{1}(\lambda) = -\frac{\lambda}{2(1+\lambda)^{4}}		a[1](lambda) = -(lambda)/(2*(1 + lambda)^(4))	Subscript[a, 1][\[Lambda]] == -Divide[\[Lambda],2*(1 + \[Lambda])^(4)]	Skipped - no semantic math	Skipped - no semantic math	-	-
11.11#Ex3	${\displaystyle{\displaystyle a_{2}(\lambda)=\frac{9\lambda^{2}-\lambda}{24(1+\lambda)^{7}}}}$ a_{2}(\lambda) = \frac{9\lambda^{2}-\lambda}{24(1+\lambda)^{7}}		a[2](lambda) = (9*(lambda)^(2)- lambda)/(24*(1 + lambda)^(7))	Subscript[a, 2][\[Lambda]] == Divide[9*\[Lambda]^(2)- \[Lambda],24*(1 + \[Lambda])^(7)]	Skipped - no semantic math	Skipped - no semantic math	-	-
11.11#Ex4	${\displaystyle{\displaystyle a_{3}(\lambda)=-\frac{225\lambda^{3}-54\lambda^{2}+\lambda}{720(1+\lambda)^{10}}}}$ a_{3}(\lambda) = -\frac{225\lambda^{3}-54\lambda^{2}+\lambda}{720(1+\lambda)^{10}}		a[3](lambda) = -(225*(lambda)^(3)- 54*(lambda)^(2)+ lambda)/(720*(1 + lambda)^(10))	Subscript[a, 3][\[Lambda]] == -Divide[225*\[Lambda]^(3)- 54*\[Lambda]^(2)+ \[Lambda],720*(1 + \[Lambda])^(10)]	Skipped - no semantic math	Skipped - no semantic math	-	-
11.11.E12	${\displaystyle{\displaystyle\mu=\sqrt{1-\lambda^{2}}-\ln\left(\frac{1+\sqrt{1-\lambda^{2}}}{\lambda}\right)}}$ \mu = \sqrt{1-\lambda^{2}}-\ln@{\frac{1+\sqrt{1-\lambda^{2}}}{\lambda}}		mu = sqrt(1 - (lambda)^(2))- ln((1 +sqrt(1 - (lambda)^(2)))/(lambda))	\[Mu] == Sqrt[1 - \[Lambda]^(2)]- Log[Divide[1 +Sqrt[1 - \[Lambda]^(2)],\[Lambda]]]	Failure	Failure	Failed [100 / 100] Result: .6584789489+.2146018366*I Test Values: {lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I} Result: -.7075464554+.5806272406*I Test Values: {lambda = 1/2*3^(1/2)+1/2*I, mu = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [100 / 100] Result: Complex[0.6584789484624085, 0.21460183660255172] Test Values: {Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.70754645532203, 0.5806272403869905] Test Values: {Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
11.11#Ex5	${\displaystyle{\displaystyle b_{0}(\lambda)=\frac{1}{(1-\lambda^{2})^{1/4}}}}$ b_{0}(\lambda) = \frac{1}{(1-\lambda^{2})^{1/4}}		b[0](lambda) = (1)/((1 - (lambda)^(2))^(1/4))	Subscript[b, 0][\[Lambda]] == Divide[1,(1 - \[Lambda]^(2))^(1/4)]	Skipped - no semantic math	Skipped - no semantic math	-	-
11.11#Ex6	${\displaystyle{\displaystyle b_{1}(\lambda)=\frac{2+3\lambda^{2}}{12(1-\lambda^{2})^{7/4}}}}$ b_{1}(\lambda) = \frac{2+3\lambda^{2}}{12(1-\lambda^{2})^{7/4}}		b[1](lambda) = (2 + 3*(lambda)^(2))/(12*(1 - (lambda)^(2))^(7/4))	Subscript[b, 1][\[Lambda]] == Divide[2 + 3*\[Lambda]^(2),12*(1 - \[Lambda]^(2))^(7/4)]	Skipped - no semantic math	Skipped - no semantic math	-	-
11.11#Ex7	${\displaystyle{\displaystyle b_{2}(\lambda)=\frac{4+300\lambda^{2}+81\lambda^{4}}{864(1-\lambda^{2})^{13/4}}}}$ b_{2}(\lambda) = \frac{4+300\lambda^{2}+81\lambda^{4}}{864(1-\lambda^{2})^{13/4}}		b[2](lambda) = (4 + 300*(lambda)^(2)+ 81*(lambda)^(4))/(864*(1 - (lambda)^(2))^(13/4))	Subscript[b, 2][\[Lambda]] == Divide[4 + 300*\[Lambda]^(2)+ 81*\[Lambda]^(4),864*(1 - \[Lambda]^(2))^(13/4)]	Skipped - no semantic math	Skipped - no semantic math	-	-