Incomplete Gamma and Related Functions - 8.21 Generalized Sine and Cosine Integrals
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 8.21.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{a-1}e^{+\iunit t}\diff{t} = e^{+\frac{1}{2}\pi\iunit a}\EulerGamma@{a}}
\int_{0}^{\infty}t^{a-1}e^{+\iunit t}\diff{t} = e^{+\frac{1}{2}\pi\iunit a}\EulerGamma@{a} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \realpart@@{a}, \realpart@@{a} < 1, \realpart@@{a} > 0} | int((t)^(a - 1)* exp(+ I*t), t = 0..infinity) = exp(+(1)/(2)*Pi*I*a)*GAMMA(a)
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Integrate[(t)^(a - 1)* Exp[+ I*t], {t, 0, Infinity}, GenerateConditions->None] == Exp[+Divide[1,2]*Pi*I*a]*Gamma[a]
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Successful | Aborted | - | Successful [Tested: 1] |
| 8.21.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{a-1}e^{-\iunit t}\diff{t} = e^{-\frac{1}{2}\pi\iunit a}\EulerGamma@{a}}
\int_{0}^{\infty}t^{a-1}e^{-\iunit t}\diff{t} = e^{-\frac{1}{2}\pi\iunit a}\EulerGamma@{a} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \realpart@@{a}, \realpart@@{a} < 1, \realpart@@{a} > 0} | int((t)^(a - 1)* exp(- I*t), t = 0..infinity) = exp(-(1)/(2)*Pi*I*a)*GAMMA(a)
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Integrate[(t)^(a - 1)* Exp[- I*t], {t, 0, Infinity}, GenerateConditions->None] == Exp[-Divide[1,2]*Pi*I*a]*Gamma[a]
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Successful | Aborted | - | Successful [Tested: 1] |