E^(a (b z^3)^(1/3)) == ((1/(3 b^(2/3) z^2)) (E^((3/2) a b^(1/3) z) (b^(2/3) z^2 + b^(1/3) z (b z^3)^(1/3) + (b z^3)^(2/3)) - ((-b^(1/3)) z + (b z^3)^(1/3)) ((2 b^(1/3) z + (b z^3)^(1/3)) Cos[(1/2) Sqrt[3] a b^(1/3) z] + Sqrt[3] (b z^3)^(1/3) Sin[(1/2) Sqrt[3] a b^(1/3) z])))/E^((1/2) a b^(1/3) z)

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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> <msup> <mi> &#8519; </mi> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mroot> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mn> 3 </mn> </mroot> </mrow> </msup> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mroot> <mi> b </mi> <mn> 3 </mn> </mroot> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; 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</mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mn> 3 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <msqrt> <mn> 3 </mn> </msqrt> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mroot> <mi> b </mi> <mn> 3 </mn> </mroot> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mroot> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mn> 3 </mn> </mroot> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mroot> <mi> b </mi> <mn> 3 </mn> </mroot> </mrow> <mo> + </mo> <mroot> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mn> 3 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; 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2007-05-02