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

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
11.11#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{0}(\lambda) = \frac{1}{1+\lambda}}
a_{0}(\lambda) = \frac{1}{1+\lambda}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{1}(\lambda) = -\frac{\lambda}{2(1+\lambda)^{4}}}
a_{1}(\lambda) = -\frac{\lambda}{2(1+\lambda)^{4}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu = \sqrt{1-\lambda^{2}}-\ln@{\frac{1+\sqrt{1-\lambda^{2}}}{\lambda}}}
\mu = \sqrt{1-\lambda^{2}}-\ln@{\frac{1+\sqrt{1-\lambda^{2}}}{\lambda}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{0}(\lambda) = \frac{1}{(1-\lambda^{2})^{1/4}}}
b_{0}(\lambda) = \frac{1}{(1-\lambda^{2})^{1/4}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 - -
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