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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(b zr+d z+e) sinhv(c z)





http://functions.wolfram.com/01.19.21.1554.01









  


  










Input Form





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










Standard Form





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MathML Form







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





2002-12-18