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 Cosh

 http://functions.wolfram.com/01.20.21.0620.01

 Input Form

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

 Standard Form

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 MathML Form

 sin m ( b z 2 + e ) cosh ( g + f z ) z ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) sinh ( g + f z ) ( - 1 2 ) m f + 2 - m - 1 2 π s = 0 m - 1 2 ( - 1 ) s ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 2 b s - b m ( cosh ( f 2 4 ( 2 b s - b m ) + g + e ( 2 s - m ) + m π 2 ) C TagBox["C", FresnelC] ( - f + 2 ( 2 b s - b m ) z 2 π 2 b s - b m ) + S TagBox["S", FresnelS] ( - f + 2 ( 2 b s - b m ) z 2 π 2 b s - b m ) sinh ( f 2 4 ( 2 b s - b m ) + g + e ( 2 s - m ) + m π 2 ) ) + 1 b m - 2 b s ( cosh ( f 2 4 ( b m - 2 b s ) + g - e ( 2 s - m ) - m π 2 ) C TagBox["C", FresnelC] ( - f + 2 ( b m - 2 b s ) z 2 π b m - 2 b s ) + S TagBox["S", FresnelS] ( - f + 2 ( b m - 2 b s ) z 2 π b m - 2 b s ) sinh ( f 2 4 ( b m - 2 b s ) + g - e ( 2 s - m ) - m π 2 ) ) ) /; m + Condition z b z 2 e m g f z Binomial m m 2 -1 1 -1 \$CellContext`m 2 g f z -1 1 2 m f -1 2 -1 m -1 1 2 1 2 s 0 m -1 2 -1 -1 s Binomial m s 1 2 b s -1 b m 1 2 -1 f 2 4 2 b s -1 b m -1 g e 2 s -1 m m 2 -1 FresnelC -1 f 2 2 b s -1 b m z 2 1 2 2 b s -1 b m 1 2 -1 FresnelS -1 f 2 2 b s -1 b m z 2 1 2 2 b s -1 b m 1 2 -1 f 2 4 2 b s -1 b m -1 g e 2 s -1 m m 2 -1 1 b m -1 2 b s 1 2 -1 f 2 4 b m -1 2 b s -1 g -1 e 2 s -1 m -1 m 2 -1 FresnelC -1 f 2 b m -1 2 b s z 2 1 2 b m -1 2 b s 1 2 -1 FresnelS -1 f 2 b m -1 2 b s z 2 1 2 b m -1 2 b s 1 2 -1 f 2 4 b m -1 2 b s -1 g -1 e 2 s -1 m -1 m 2 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18