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http://functions.wolfram.com/01.20.21.1909.01
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Integrate[Cos[a z^2 + p z + q] Sinh[w z^2 + s z + t] Cosh[c z^2 + f z + g],
z] == (E^(g - I q + t - (-f^2 + 2 I f p + p^2 - 2 f s + 2 I p s - s^2)/
(4 (I a - c - w))) Sqrt[Pi]
Erf[(-f + I p - s + 2 I a z - 2 c z - 2 w z)/(2 Sqrt[I a - c - w])])/
(16 Sqrt[I a - c - w]) +
(E^(-g - I q + t - (-f^2 - 2 I f p + p^2 + 2 f s + 2 I p s - s^2)/
(4 (I a + c - w))) Sqrt[Pi]
Erf[(f + I p - s + 2 I a z + 2 c z - 2 w z)/(2 Sqrt[I a + c - w])])/
(16 Sqrt[I a + c - w]) -
(E^(g - I q - t - (-f^2 + 2 I f p + p^2 + 2 f s - 2 I p s - s^2)/
(4 (I a - c + w))) Sqrt[Pi]
Erf[(-f + I p + s + 2 I a z - 2 c z + 2 w z)/(2 Sqrt[I a - c + w])])/
(16 Sqrt[I a - c + w]) -
(E^(-g - I q - t - (-f^2 - 2 I f p + p^2 - 2 f s - 2 I p s - s^2)/
(4 (I a + c + w))) Sqrt[Pi]
Erf[(f + I p + s + 2 I a z + 2 c z + 2 w z)/(2 Sqrt[I a + c + w])])/
(16 Sqrt[I a + c + w]) -
(E^(-g + I q + t - (f^2 - 2 I f p - p^2 - 2 f s + 2 I p s + s^2)/
(4 (I a - c + w))) Sqrt[Pi]
Erfi[(f - I p - s - 2 I a z + 2 c z - 2 w z)/(2 Sqrt[I a - c + w])])/
(16 Sqrt[I a - c + w]) -
(E^(g + I q - t - (f^2 + 2 I f p - p^2 - 2 f s - 2 I p s + s^2)/
(4 (I a + c - w))) Sqrt[Pi]
Erfi[(f + I p - s + 2 I a z + 2 c z - 2 w z)/(2 Sqrt[I a + c - w])])/
(16 Sqrt[I a + c - w]) +
(E^(-g + I q - t - (f^2 - 2 I f p - p^2 + 2 f s - 2 I p s + s^2)/
(4 (I a - c - w))) Sqrt[Pi]
Erfi[(f - I p + s - 2 I a z + 2 c z + 2 w z)/(2 Sqrt[I a - c - w])])/
(16 Sqrt[I a - c - w]) +
(E^(g + I q + t - (f^2 + 2 I f p - p^2 + 2 f s + 2 I p s + s^2)/
(4 (I a + c + w))) Sqrt[Pi]
Erfi[(f + I p + s + 2 I a z + 2 c z + 2 w z)/(2 Sqrt[I a + c + w])])/
(16 Sqrt[I a + c + w])
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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> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> s </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> t </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> g </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> g </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> + </mo> <mi> t </mi> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <msup> <mi> f </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> + </mo> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> s </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> f </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mi> g </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> + </mo> <mi> t </mi> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <msup> <mi> f </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> + </mo> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> s </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mi> g </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> - </mo> <mi> t </mi> <mo> - </mo> <mfrac> <mrow> <msup> <mi> f </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> - </mo> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> s </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> g </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> + </mo> <mi> t </mi> <mo> - </mo> <mfrac> <mrow> <msup> <mi> f </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> - </mo> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> s </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> g </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> - </mo> <mi> t </mi> <mo> - </mo> <mfrac> <mrow> <msup> <mi> f </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> - </mo> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> s </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> g </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> - </mo> <mi> t </mi> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <msup> <mi> f </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> + </mo> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> s </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> f </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mi> g </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> + </mo> <mi> t </mi> <mo> - </mo> <mfrac> <mrow> <msup> <mi> f </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> - </mo> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> s </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mi> g </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> - </mo> <mi> t </mi> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <msup> <mi> f </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> + </mo> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> s </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> 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</apply> <apply> <power /> <ci> p </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> s </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erf </ci> <apply> <times /> <apply> <plus /> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> w </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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