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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and trigonometric functions > Involving sin and sinh > Involving sin(a zr+p z+q)sinh(w zr+s z+t) cosh( c zr+f z+g)





http://functions.wolfram.com/01.20.21.1891.01









  


  










Input Form





Integrate[Sin[a z^2 + p z + q] Sinh[w z^2 + s z + t] Cosh[c z^2 + f z + g], z] == (-I) (-((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]))










Standard Form





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MathML Form







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</mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> g </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> f </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erf </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> f </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mi> g </mi> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> f </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erf </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mi> g </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> f </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> g </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> f </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mi> g </mi> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> f </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erf </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> g </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> f </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <msqrt> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mi> g </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> f </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> <mo> &#8290; </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> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> 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<apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <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> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> w </ci> <ci> z </ci> </apply> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18