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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function and a power function > Involving products of powers of the direct function and a power function > Involving product of power of the direct function, the direct function and a power function > Involving zalpha-1 sin(b zr+e) sinv(c zr)





http://functions.wolfram.com/01.06.21.1159.01









  


  










Input Form





Integrate[z^n Sin[b Sqrt[z] + e] Sin[c Sqrt[z]]^v, z] == ((-1)^n Binomial[v, v/2] (E^(I e - (I Pi)/2) Gamma[2 (1 + n), (-I) b Sqrt[z]] + E^((-I) e + (I Pi)/2) Gamma[2 (1 + n), I b Sqrt[z]]) (1 - Mod[v, 2]))/(2^v b^(2 (1 + n))) - Sum[(-1)^s Binomial[v, s] ((E^(I e - (1/2) I Pi (1 + v)) Gamma[2 (1 + n), ((-I) b - I c (-2 s + v)) Sqrt[z]])/ ((-I) b - I c (-2 s + v))^(2 (1 + n)) + (E^((-I) e + (1/2) I Pi (1 - v)) Gamma[2 (1 + n), (I b - I c (-2 s + v)) Sqrt[z]])/(I b - I c (-2 s + v))^ (2 (1 + n)) + (E^(I e - (1/2) I Pi (1 - v)) Gamma[2 (1 + n), ((-I) b + I c (-2 s + v)) Sqrt[z]])/((-I) b + I c (-2 s + v))^ (2 (1 + n)) + (E^((-I) e + (1/2) I Pi (1 + v)) Gamma[2 (1 + n), (I b + I c (-2 s + v)) Sqrt[z]])/ (I b + I c (-2 s + v))^(2 (1 + n))), {s, 0, Floor[(1/2) (-1 + v)]}]/ 2^v /; Element[n, Integers] && n >= 0 && 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