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Csch






Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic, exponential and trigonometric functions > Involving cos, sinh and exp > Involving ep z cos(a z)sinh(b z) csch( c z)





http://functions.wolfram.com/01.23.21.0248.01









  


  










Input Form





Integrate[E^(p z) Cos[a z] Sinh[b z] Csch[c z], z] == (E^((I a + b) z) (E^((-I) a z) + E^(I a z)) (-E^((-b) z) + E^(b z)) (1 - E^(2 c z)) ((1/(I a + b - c - p)) (E^(((-I) a - b + c + p) z) Hypergeometric2F1[1, ((-I) a - b + c + p)/(2 c), ((-I) a - b + 3 c + p)/(2 c), E^(2 c z)]) - (1/(I a - b + c + p)) (E^((I a - b + c + p) z) Hypergeometric2F1[1, (I a - b + c + p)/(2 c), (I a - b + 3 c + p)/(2 c), E^(2 c z)]) + I ((E^(((-I) a + b + c + p) z) Hypergeometric2F1[1, ((-I) a + b + c + p)/ (2 c), ((-I) a + b + 3 c + p)/(2 c), E^(2 c z)])/ (a + I (b + c + p)) - (E^((I a + b + c + p) z) Hypergeometric2F1[1, (I a + b + c + p)/(2 c), (I a + b + 3 c + p)/(2 c), E^(2 c z)])/ (a - I (b + c + p)))))/(2 (1 + E^(2 I a z)) (-1 + E^(2 b z)) (-1 + E^(2 c z)))










Standard Form





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MathML Form







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<mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> p </mi> </mrow> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> p </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> p </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> ; </mo> <msup> <mi> &#8519; </mi> <mrow> <mn> 2 </mn> <mo> 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<ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18