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http://functions.wolfram.com/01.03.21.0384.01
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Integrate[(E^(d z + e))^\[Mu] (E^(Sqrt[z] c))^\[Nu], z] ==
(1/(2 (d \[Mu])^(3/2))) (((E^(c Sqrt[z]))^\[Nu] (E^(e + d z))^\[Mu]
(2 E^((2 d Sqrt[z] \[Mu] + c \[Nu])^2/(4 d \[Mu])) Sqrt[d \[Mu]] -
c Sqrt[Pi] \[Nu] Erfi[(2 d Sqrt[z] \[Mu] + c \[Nu])/(2 Sqrt[d \[Mu]])]))/
E^((2 d Sqrt[z] \[Mu] + c \[Nu])^2/(4 d \[Mu])))
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> + </mo> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> </msup> <mo> ) </mo> </mrow> <mi> μ </mi> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mi> c </mi> </mrow> </msup> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> d </mi> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mi> μ </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> d </mi> <mo> ⁢ </mo> <mi> μ </mi> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> c </mi> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> + </mo> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> </msup> <mo> ) </mo> </mrow> <mi> μ </mi> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> d </mi> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mi> μ </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> d </mi> <mo> ⁢ </mo> <mi> μ </mi> </mrow> </mfrac> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> μ </mi> </mrow> </msqrt> </mrow> <mo> - 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Date Added to functions.wolfram.com (modification date)
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