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Sech






Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic and exponential functions > Involving powers of the direct function, hyperbolic and exponential functions > Involving powers of sinh and exp > Involving ep z sinhu(b z) sechnu(c z)





http://functions.wolfram.com/01.24.21.0496.01









  


  










Input Form





Integrate[E^(p z) Sinh[c z]^\[Mu] Sech[c z]^\[Nu], z] == ((1/(p + c (\[Mu] - \[Nu]))) E^(p z) (1 + E^(-2 c z))^\[Nu] AppellF1[-((p + c \[Mu] - c \[Nu])/(2 c)), \[Nu], -\[Mu], (-p + c (2 - \[Mu] + \[Nu]))/(2 c), -E^(-2 c z), E^(-2 c z)] Sech[c z]^\[Nu] Sinh[c z]^\[Mu])/(1 - E^(-2 c z))^\[Mu]










Standard Form





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MathML Form







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</mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> </mrow> <mo> , </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> p </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <sinh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <ci> &#956; </ci> </apply> <apply> <power /> <apply> <sech /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> p </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <ci> &#957; </ci> </apply> <apply> <power /> <apply> <sech /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <ci> &#957; </ci> </apply> <apply> <power /> <apply> <sinh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <ci> &#956; </ci> </apply> <apply> <power /> <apply> <plus /> <ci> p </ci> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> &#956; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> AppellF1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <ci> c </ci> <ci> &#956; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> c </ci> <ci> z </ci> </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