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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving products of powers of the direct function > Involving product of power of the direct function and the direct function > Involving sinh(d z+e) sinhv(c zr)





http://functions.wolfram.com/01.19.21.1566.01









  


  










Input Form





Integrate[Sinh[d z + e] Sinh[c z^2]^v, z] == (1/d) ((Binomial[v, v/2] (1 - Mod[v, 2]) Cosh[e + d z])/(I^v 2^v)) + I^(1 + v) 2^(-(1/2) - v) Sqrt[Pi] Sum[(-1)^s Binomial[v, s] ((Sinh[e - (1/2) I Pi v + d^2/(4 (2 c s - c v))] FresnelC[(-d + 2 (2 c s - c v) z)/(Sqrt[2 Pi] Sqrt[2 I c s - I c v])] - I FresnelS[(-d + 2 (2 c s - c v) z)/ (Sqrt[2 Pi] Sqrt[2 I c s - I c v])] Cosh[e - (1/2) I Pi v + d^2/(4 (2 c s - c v))])/Sqrt[2 I c s - I c v] + (Sinh[e + (1/2) I Pi v + d^2/(4 (-2 c s + c v))] FresnelC[(-d + 2 (-2 c s + c v) z)/(Sqrt[2 Pi] Sqrt[-2 I c s + I c v])] - I FresnelS[(-d + 2 (-2 c s + c v) z)/ (Sqrt[2 Pi] Sqrt[-2 I c s + I c v])] Cosh[e + (1/2) I Pi v + d^2/(4 (-2 c s + c v))])/Sqrt[-2 I c s + I c v]), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0










Standard Form





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MathML Form







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Rule Form





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





2002-12-18