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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power > Involving zn eb zr+d z+e sinh(c zr+g)





http://functions.wolfram.com/01.19.21.0400.01









  


  










Input Form





Integrate[z^n E^(b Sqrt[z] + d z + e) Sinh[c Sqrt[z] + g], z] == 2^(-2 - 2 n) d^(-2 - 2 n) ((-E^(-((b - c)^2/(4 d)) + e - g)) Sum[(-1)^(-h + k) 4^k (b - c)^(-h - k + 2 n) (b - c + 2 d Sqrt[z])^ (h + k) (-((b - c + 2 d Sqrt[z])^2/d))^((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] ((b - c) (b - c + 2 d Sqrt[z]) Gamma[(1/2) (1 + h + k), -((b - c + 2 d Sqrt[z])^2/(4 d))] + 2 d Sqrt[-((b - c + 2 d Sqrt[z])^2/d)] Gamma[(1/2) (2 + h + k), -((b - c + 2 d Sqrt[z])^2/(4 d))]), {k, 0, n}, {h, 0, k}] + E^(-((b + c)^2/(4 d)) + e + g) Sum[(-1)^(-h + k) 4^k (b + c)^(-h - k + 2 n) (b + c + 2 d Sqrt[z])^(h + k) (-((b + c + 2 d Sqrt[z])^2/d))^((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] ((b + c) (b + c + 2 d Sqrt[z]) Gamma[(1/2) (1 + h + k), -((b + c + 2 d Sqrt[z])^2/(4 d))] + 2 d Sqrt[-((b + c + 2 d Sqrt[z])^2/d)] Gamma[(1/2) (2 + h + k), -((b + c + 2 d Sqrt[z])^2/(4 d))]), {k, 0, n}, {h, 0, k}]) /; Element[n, Integers] && n >= 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