Error Functions, Dawson’s and Fresnel Integrals - 7.4 Symmetry

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
7.4.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@{-z} = -\erf@{z}}
\erf@{-z} = -\erf@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
erf(- z) = - erf(z)

Erf[- z] == - Erf[z]
Successful Successful - Successful [Tested: 7]
7.4.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@{-z} = 2-\erfc@{z}}
\erfc@{-z} = 2-\erfc@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
erfc(- z) = 2 - erfc(z)

Erfc[- z] == 2 - Erfc[z]
Successful Successful - Successful [Tested: 7]
7.4.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \DawsonsintF@{-z} = -\DawsonsintF@{z}}
\DawsonsintF@{-z} = -\DawsonsintF@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
dawson(- z) = - dawson(z)

DawsonF[- z] == - DawsonF[z]
Successful Successful - Successful [Tested: 7]
7.4#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{-z} = -\Fresnelcosint@{z}}
\Fresnelcosint@{-z} = -\Fresnelcosint@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
FresnelC(- z) = - FresnelC(z)

FresnelC[- z] == - FresnelC[z]
Successful Successful - Successful [Tested: 7]
7.4#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{-z} = -\Fresnelsinint@{z}}
\Fresnelsinint@{-z} = -\Fresnelsinint@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
FresnelS(- z) = - FresnelS(z)

FresnelS[- z] == - FresnelS[z]
Successful Successful - Successful [Tested: 7]
7.4#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{iz} = i\Fresnelcosint@{z}}
\Fresnelcosint@{iz} = i\Fresnelcosint@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
FresnelC(I*z) = I*FresnelC(z)

FresnelC[I*z] == I*FresnelC[z]
Successful Successful - Successful [Tested: 7]
7.4#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{iz} = -i\Fresnelsinint@{z}}
\Fresnelsinint@{iz} = -i\Fresnelsinint@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
FresnelS(I*z) = - I*FresnelS(z)

FresnelS[I*z] == - I*FresnelS[z]
Successful Successful - Successful [Tested: 7]
7.4#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelf@{iz} = (1/\sqrt{2})e^{\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}-i\auxFresnelf@{z}}
\auxFresnelf@{iz} = (1/\sqrt{2})e^{\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}-i\auxFresnelf@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
Fresnelf(I*z) = (1/(sqrt(2)))*exp((1)/(4)*Pi*I -(1)/(2)*Pi*I*(z)^(2))- I*Fresnelf(z)

FresnelF[I*z] == (1/(Sqrt[2]))*Exp[Divide[1,4]*Pi*I -Divide[1,2]*Pi*I*(z)^(2)]- I*FresnelF[z]
Failure Failure Successful [Tested: 7] Successful [Tested: 7]
7.4#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelg@{iz} = (1/\sqrt{2})e^{-\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}+i\auxFresnelg@{z}}
\auxFresnelg@{iz} = (1/\sqrt{2})e^{-\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}+i\auxFresnelg@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
Fresnelg(I*z) = (1/(sqrt(2)))*exp(-(1)/(4)*Pi*I -(1)/(2)*Pi*I*(z)^(2))+ I*Fresnelg(z)

FresnelG[I*z] == (1/(Sqrt[2]))*Exp[-Divide[1,4]*Pi*I -Divide[1,2]*Pi*I*(z)^(2)]+ I*FresnelG[z]
Failure Failure Successful [Tested: 7] Successful [Tested: 7]
7.4#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelf@{-z} = \sqrt{2}\cos@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelf@{z}}
\auxFresnelf@{-z} = \sqrt{2}\cos@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelf@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
Fresnelf(- z) = sqrt(2)*cos((1)/(4)*Pi +(1)/(2)*Pi*(z)^(2))- Fresnelf(z)

FresnelF[- z] == Sqrt[2]*Cos[Divide[1,4]*Pi +Divide[1,2]*Pi*(z)^(2)]- FresnelF[z]
Successful Successful - Successful [Tested: 7]
7.4#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelg@{-z} = \sqrt{2}\sin@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelg@{z}}
\auxFresnelg@{-z} = \sqrt{2}\sin@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelg@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
Fresnelg(- z) = sqrt(2)*sin((1)/(4)*Pi +(1)/(2)*Pi*(z)^(2))- Fresnelg(z)

FresnelG[- z] == Sqrt[2]*Sin[Divide[1,4]*Pi +Divide[1,2]*Pi*(z)^(2)]- FresnelG[z]
Successful Failure - Successful [Tested: 7]
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