12.13: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/12.13.E1 12.13.E1] || [[Item:Q4230|<math>\paraU@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{(-y)^{m}}{m!}\paraU@{a-m}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\paraU@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{(-y)^{m}}{m!}\paraU@{a-m}{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>CylinderU(a, x + y) = exp((1)/(2)*x*y +(1)/(4)*(y)^(2))*sum(((- y)^(m))/(factorial(m))*CylinderU(a - m, x), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ParabolicCylinderD[- 1/2 -(a), x + y] == Exp[Divide[1,2]*x*y +Divide[1,4]*(y)^(2)]*Sum[Divide[(- y)^(m),(m)!]*ParabolicCylinderD[- 1/2 -(a - m), x], {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
| [https://dlmf.nist.gov/12.13.E1 12.13.E1] || <math qid="Q4230">\paraU@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{(-y)^{m}}{m!}\paraU@{a-m}{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\paraU@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{(-y)^{m}}{m!}\paraU@{a-m}{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>CylinderU(a, x + y) = exp((1)/(2)*x*y +(1)/(4)*(y)^(2))*sum(((- y)^(m))/(factorial(m))*CylinderU(a - m, x), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ParabolicCylinderD[- 1/2 -(a), x + y] == Exp[Divide[1,2]*x*y +Divide[1,4]*(y)^(2)]*Sum[Divide[(- y)^(m),(m)!]*ParabolicCylinderD[- 1/2 -(a - m), x], {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/12.13.E2 12.13.E2] || [[Item:Q4231|<math>\paraU@{a}{x+y} = e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}y^{m}\paraU@{a+m}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\paraU@{a}{x+y} = e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}y^{m}\paraU@{a+m}{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>CylinderU(a, x + y) = exp(-(1)/(2)*x*y -(1)/(4)*(y)^(2))*sum(binomial(- a -(1)/(2),m)*(y)^(m)* CylinderU(a + m, x), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ParabolicCylinderD[- 1/2 -(a), x + y] == Exp[-Divide[1,2]*x*y -Divide[1,4]*(y)^(2)]*Sum[Binomial[- a -Divide[1,2],m]*(y)^(m)* ParabolicCylinderD[- 1/2 -(a + m), x], {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
| [https://dlmf.nist.gov/12.13.E2 12.13.E2] || <math qid="Q4231">\paraU@{a}{x+y} = e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}y^{m}\paraU@{a+m}{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\paraU@{a}{x+y} = e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}y^{m}\paraU@{a+m}{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>CylinderU(a, x + y) = exp(-(1)/(2)*x*y -(1)/(4)*(y)^(2))*sum(binomial(- a -(1)/(2),m)*(y)^(m)* CylinderU(a + m, x), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ParabolicCylinderD[- 1/2 -(a), x + y] == Exp[-Divide[1,2]*x*y -Divide[1,4]*(y)^(2)]*Sum[Binomial[- a -Divide[1,2],m]*(y)^(m)* ParabolicCylinderD[- 1/2 -(a + m), x], {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/12.13.E3 12.13.E3] || [[Item:Q4232|<math>\paraV@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\binom{a-\tfrac{1}{2}}{m}y^{m}\paraV@{a-m}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\paraV@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\binom{a-\tfrac{1}{2}}{m}y^{m}\paraV@{a-m}{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>CylinderV(a, x + y) = exp((1)/(2)*x*y +(1)/(4)*(y)^(2))*sum(binomial(a -(1)/(2),m)*(y)^(m)* CylinderV(a - m, x), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[GAMMA[1/2 + a], Pi]*(Sin[Pi*(a)] * ParabolicCylinderD[-(a) - 1/2, x + y] + ParabolicCylinderD[-(a) - 1/2, -(x + y)]) == Exp[Divide[1,2]*x*y +Divide[1,4]*(y)^(2)]*Sum[Binomial[a -Divide[1,2],m]*(y)^(m)* Divide[GAMMA[1/2 + a - m], Pi]*(Sin[Pi*(a - m)] * ParabolicCylinderD[-(a - m) - 1/2, x] + ParabolicCylinderD[-(a - m) - 1/2, -(x)]), {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
| [https://dlmf.nist.gov/12.13.E3 12.13.E3] || <math qid="Q4232">\paraV@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\binom{a-\tfrac{1}{2}}{m}y^{m}\paraV@{a-m}{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\paraV@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\binom{a-\tfrac{1}{2}}{m}y^{m}\paraV@{a-m}{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>CylinderV(a, x + y) = exp((1)/(2)*x*y +(1)/(4)*(y)^(2))*sum(binomial(a -(1)/(2),m)*(y)^(m)* CylinderV(a - m, x), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[GAMMA[1/2 + a], Pi]*(Sin[Pi*(a)] * ParabolicCylinderD[-(a) - 1/2, x + y] + ParabolicCylinderD[-(a) - 1/2, -(x + y)]) == Exp[Divide[1,2]*x*y +Divide[1,4]*(y)^(2)]*Sum[Binomial[a -Divide[1,2],m]*(y)^(m)* Divide[GAMMA[1/2 + a - m], Pi]*(Sin[Pi*(a - m)] * ParabolicCylinderD[-(a - m) - 1/2, x] + ParabolicCylinderD[-(a - m) - 1/2, -(x)]), {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/12.13.E4 12.13.E4] || [[Item:Q4233|<math>\paraV@{a}{x+y} = e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{y^{m}}{m!}\paraV@{a+m}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\paraV@{a}{x+y} = e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{y^{m}}{m!}\paraV@{a+m}{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>CylinderV(a, x + y) = exp(-(1)/(2)*x*y -(1)/(4)*(y)^(2))*sum(((y)^(m))/(factorial(m))*CylinderV(a + m, x), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[GAMMA[1/2 + a], Pi]*(Sin[Pi*(a)] * ParabolicCylinderD[-(a) - 1/2, x + y] + ParabolicCylinderD[-(a) - 1/2, -(x + y)]) == Exp[-Divide[1,2]*x*y -Divide[1,4]*(y)^(2)]*Sum[Divide[(y)^(m),(m)!]*Divide[GAMMA[1/2 + a + m], Pi]*(Sin[Pi*(a + m)] * ParabolicCylinderD[-(a + m) - 1/2, x] + ParabolicCylinderD[-(a + m) - 1/2, -(x)]), {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
| [https://dlmf.nist.gov/12.13.E4 12.13.E4] || <math qid="Q4233">\paraV@{a}{x+y} = e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{y^{m}}{m!}\paraV@{a+m}{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\paraV@{a}{x+y} = e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{y^{m}}{m!}\paraV@{a+m}{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>CylinderV(a, x + y) = exp(-(1)/(2)*x*y -(1)/(4)*(y)^(2))*sum(((y)^(m))/(factorial(m))*CylinderV(a + m, x), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[GAMMA[1/2 + a], Pi]*(Sin[Pi*(a)] * ParabolicCylinderD[-(a) - 1/2, x + y] + ParabolicCylinderD[-(a) - 1/2, -(x + y)]) == Exp[-Divide[1,2]*x*y -Divide[1,4]*(y)^(2)]*Sum[Divide[(y)^(m),(m)!]*Divide[GAMMA[1/2 + a + m], Pi]*(Sin[Pi*(a + m)] * ParabolicCylinderD[-(a + m) - 1/2, x] + ParabolicCylinderD[-(a + m) - 1/2, -(x)]), {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/12.13.E5 12.13.E5] || [[Item:Q4234|<math>\paraU@{a}{x\cos@@{t}+y\sin@@{t}}\\ = e^{\frac{1}{4}(x\sin@@{t}-y\cos@@{t})^{2}}\*\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}(\tan@@{t})^{m}\paraU@{m+a}{x}\paraU@{-m-\tfrac{1}{2}}{y}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\paraU@{a}{x\cos@@{t}+y\sin@@{t}}\\ = e^{\frac{1}{4}(x\sin@@{t}-y\cos@@{t})^{2}}\*\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}(\tan@@{t})^{m}\paraU@{m+a}{x}\paraU@{-m-\tfrac{1}{2}}{y}</syntaxhighlight> || <math>\realpart@@{a} \leq -\tfrac{1}{2}, 0 \leq t, t \leq \tfrac{1}{4}\pi</math> || <syntaxhighlight lang=mathematica>CylinderU(a, x*cos(t)+ y*sin(t)) = exp((1)/(4)*(x*sin(t)- y*cos(t))^(2))* sum(binomial(- a -(1)/(2),m)*(tan(t))^(m)* CylinderU(m + a, x)*CylinderU(- m -(1)/(2), y), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ParabolicCylinderD[- 1/2 -(a), x*Cos[t]+ y*Sin[t]] == Exp[Divide[1,4]*(x*Sin[t]- y*Cos[t])^(2)]* Sum[Binomial[- a -Divide[1,2],m]*(Tan[t])^(m)* ParabolicCylinderD[- 1/2 -(m + a), x]*ParabolicCylinderD[- 1/2 -(- m -Divide[1,2]), y], {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skip - No test values generated
| [https://dlmf.nist.gov/12.13.E5 12.13.E5] || <math qid="Q4234">\paraU@{a}{x\cos@@{t}+y\sin@@{t}}\\ = e^{\frac{1}{4}(x\sin@@{t}-y\cos@@{t})^{2}}\*\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}(\tan@@{t})^{m}\paraU@{m+a}{x}\paraU@{-m-\tfrac{1}{2}}{y}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\paraU@{a}{x\cos@@{t}+y\sin@@{t}}\\ = e^{\frac{1}{4}(x\sin@@{t}-y\cos@@{t})^{2}}\*\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}(\tan@@{t})^{m}\paraU@{m+a}{x}\paraU@{-m-\tfrac{1}{2}}{y}</syntaxhighlight> || <math>\realpart@@{a} \leq -\tfrac{1}{2}, 0 \leq t, t \leq \tfrac{1}{4}\pi</math> || <syntaxhighlight lang=mathematica>CylinderU(a, x*cos(t)+ y*sin(t)) = exp((1)/(4)*(x*sin(t)- y*cos(t))^(2))* sum(binomial(- a -(1)/(2),m)*(tan(t))^(m)* CylinderU(m + a, x)*CylinderU(- m -(1)/(2), y), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ParabolicCylinderD[- 1/2 -(a), x*Cos[t]+ y*Sin[t]] == Exp[Divide[1,4]*(x*Sin[t]- y*Cos[t])^(2)]* Sum[Binomial[- a -Divide[1,2],m]*(Tan[t])^(m)* ParabolicCylinderD[- 1/2 -(m + a), x]*ParabolicCylinderD[- 1/2 -(- m -Divide[1,2]), y], {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skip - No test values generated
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Latest revision as of 11:31, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
12.13.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{(-y)^{m}}{m!}\paraU@{a-m}{x}}
\paraU@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{(-y)^{m}}{m!}\paraU@{a-m}{x}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
CylinderU(a, x + y) = exp((1)/(2)*x*y +(1)/(4)*(y)^(2))*sum(((- y)^(m))/(factorial(m))*CylinderU(a - m, x), m = 0..infinity)

ParabolicCylinderD[- 1/2 -(a), x + y] == Exp[Divide[1,2]*x*y +Divide[1,4]*(y)^(2)]*Sum[Divide[(- y)^(m),(m)!]*ParabolicCylinderD[- 1/2 -(a - m), x], {m, 0, Infinity}, GenerateConditions->None]
Failure Failure Skipped - Because timed out Skipped - Because timed out
12.13.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{x+y} = e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}y^{m}\paraU@{a+m}{x}}
\paraU@{a}{x+y} = e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}y^{m}\paraU@{a+m}{x}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
CylinderU(a, x + y) = exp(-(1)/(2)*x*y -(1)/(4)*(y)^(2))*sum(binomial(- a -(1)/(2),m)*(y)^(m)* CylinderU(a + m, x), m = 0..infinity)

ParabolicCylinderD[- 1/2 -(a), x + y] == Exp[-Divide[1,2]*x*y -Divide[1,4]*(y)^(2)]*Sum[Binomial[- a -Divide[1,2],m]*(y)^(m)* ParabolicCylinderD[- 1/2 -(a + m), x], {m, 0, Infinity}, GenerateConditions->None]
Failure Failure Skipped - Because timed out Skipped - Because timed out
12.13.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\binom{a-\tfrac{1}{2}}{m}y^{m}\paraV@{a-m}{x}}
\paraV@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\binom{a-\tfrac{1}{2}}{m}y^{m}\paraV@{a-m}{x}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
CylinderV(a, x + y) = exp((1)/(2)*x*y +(1)/(4)*(y)^(2))*sum(binomial(a -(1)/(2),m)*(y)^(m)* CylinderV(a - m, x), m = 0..infinity)

Divide[GAMMA[1/2 + a], Pi]*(Sin[Pi*(a)] * ParabolicCylinderD[-(a) - 1/2, x + y] + ParabolicCylinderD[-(a) - 1/2, -(x + y)]) == Exp[Divide[1,2]*x*y +Divide[1,4]*(y)^(2)]*Sum[Binomial[a -Divide[1,2],m]*(y)^(m)* Divide[GAMMA[1/2 + a - m], Pi]*(Sin[Pi*(a - m)] * ParabolicCylinderD[-(a - m) - 1/2, x] + ParabolicCylinderD[-(a - m) - 1/2, -(x)]), {m, 0, Infinity}, GenerateConditions->None]
Failure Failure Skipped - Because timed out Skipped - Because timed out
12.13.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV@{a}{x+y} = e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{y^{m}}{m!}\paraV@{a+m}{x}}
\paraV@{a}{x+y} = e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{y^{m}}{m!}\paraV@{a+m}{x}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
CylinderV(a, x + y) = exp(-(1)/(2)*x*y -(1)/(4)*(y)^(2))*sum(((y)^(m))/(factorial(m))*CylinderV(a + m, x), m = 0..infinity)

Divide[GAMMA[1/2 + a], Pi]*(Sin[Pi*(a)] * ParabolicCylinderD[-(a) - 1/2, x + y] + ParabolicCylinderD[-(a) - 1/2, -(x + y)]) == Exp[-Divide[1,2]*x*y -Divide[1,4]*(y)^(2)]*Sum[Divide[(y)^(m),(m)!]*Divide[GAMMA[1/2 + a + m], Pi]*(Sin[Pi*(a + m)] * ParabolicCylinderD[-(a + m) - 1/2, x] + ParabolicCylinderD[-(a + m) - 1/2, -(x)]), {m, 0, Infinity}, GenerateConditions->None]
Failure Failure Skipped - Because timed out Skipped - Because timed out
12.13.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{x\cos@@{t}+y\sin@@{t}}\\ = e^{\frac{1}{4}(x\sin@@{t}-y\cos@@{t})^{2}}\*\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}(\tan@@{t})^{m}\paraU@{m+a}{x}\paraU@{-m-\tfrac{1}{2}}{y}}
\paraU@{a}{x\cos@@{t}+y\sin@@{t}}\\ = e^{\frac{1}{4}(x\sin@@{t}-y\cos@@{t})^{2}}\*\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}(\tan@@{t})^{m}\paraU@{m+a}{x}\paraU@{-m-\tfrac{1}{2}}{y}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{a} \leq -\tfrac{1}{2}, 0 \leq t, t \leq \tfrac{1}{4}\pi} 
CylinderU(a, x*cos(t)+ y*sin(t)) = exp((1)/(4)*(x*sin(t)- y*cos(t))^(2))* sum(binomial(- a -(1)/(2),m)*(tan(t))^(m)* CylinderU(m + a, x)*CylinderU(- m -(1)/(2), y), m = 0..infinity)

ParabolicCylinderD[- 1/2 -(a), x*Cos[t]+ y*Sin[t]] == Exp[Divide[1,4]*(x*Sin[t]- y*Cos[t])^(2)]* Sum[Binomial[- a -Divide[1,2],m]*(Tan[t])^(m)* ParabolicCylinderD[- 1/2 -(m + a), x]*ParabolicCylinderD[- 1/2 -(- m -Divide[1,2]), y], {m, 0, Infinity}, GenerateConditions->None]
Failure Failure Skipped - Because timed out Skip - No test values generated
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