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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power function > Involving power > Involving zalpha-1and arguments a z+b





http://functions.wolfram.com/01.19.21.0072.01









  


  










Input Form





Integrate[z^(n + 1/2) Sinh[a z + b], z] == (((-1)^n a^(-1 - n) Sqrt[z])/(E^b (2 Sqrt[(-a^2) z^2]))) (Gamma[3/2 + n] (E^(2 b) Sqrt[a z] Erfc[Sqrt[(-a) z]] + (-1)^n Sqrt[(-a) z] Erfc[Sqrt[a z]]) + Sqrt[a z] E^(a z + 2 b) (Sum[((-a) z)^(1/2 + k)/Pochhammer[3/2 + n, k - n], {k, 0, n}] - Sum[((-a) z)^(1/2 + k)/Pochhammer[3/2 + n, k - n], {k, 1 + n, -1}]) + ((-1)^n Sqrt[(-a) z] (Sum[(a z)^(1/2 + k)/Pochhammer[3/2 + n, k - n], {k, 0, n}] - Sum[(a z)^(1/2 + k)/Pochhammer[3/2 + n, k - n], {k, 1 + n, -1}]))/E^(a z)) /; Element[n, Integers]










Standard Form





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MathML Form







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</apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18