html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.4112.01

 Input Form

 Integrate[Sinh[b Sqrt[z] + d z + e] Cosh[c Sqrt[z] + f z + g]^v, z] == (-(1/((-I) d)^(3/2))) 2^(-1 - v) Binomial[v, v/2] (1 - Mod[v, 2]) (2 I Sqrt[(-I) d] Cosh[e + b Sqrt[z] + d z] - b Sqrt[2 Pi] (I Cosh[b^2/(4 d) - e] FresnelS[(-b - 2 d Sqrt[z])/ (Sqrt[(-I) d] Sqrt[2 Pi])] + FresnelC[(-b - 2 d Sqrt[z])/(Sqrt[(-I) d] Sqrt[2 Pi])] Sinh[b^2/(4 d) - e])) + 2^(-1 - v) Sum[Binomial[v, s] ((-2 I Sqrt[I (-d - 2 f s + f v)] Cosh[e + 2 g s - g v - (-b - 2 c s + c v) Sqrt[z] - (-d - 2 f s + f v) z] - Sqrt[2 Pi] (-b - 2 c s + c v) (I Cosh[e + 2 g s - g v + (-b - 2 c s + c v)^2/(-4 d - 8 f s + 4 f v)] FresnelS[(-b - 2 c s + c v + 2 (-d - 2 f s + f v) Sqrt[z])/(Sqrt[2 Pi] Sqrt[I (-d - 2 f s + f v)])] - FresnelC[(-b - 2 c s + c v + 2 (-d - 2 f s + f v) Sqrt[z])/ (Sqrt[2 Pi] Sqrt[I (-d - 2 f s + f v)])] Sinh[e + 2 g s - g v + (-b - 2 c s + c v)^2/(-4 d - 8 f s + 4 f v)]))/(I (-d - 2 f s + f v))^(3/2) + (-2 I Sqrt[I (-d + 2 f s - f v)] Cosh[e - 2 g s + g v - (-b + 2 c s - c v) Sqrt[z] - (-d + 2 f s - f v) z] - Sqrt[2 Pi] (-b + 2 c s - c v) (I Cosh[e - 2 g s + g v + (b + c (-2 s + v))^2/(-4 d + 8 f s - 4 f v)] FresnelS[(-b + 2 c s - c v + 2 (-d + 2 f s - f v) Sqrt[z])/(Sqrt[2 Pi] Sqrt[I (-d + 2 f s - f v)])] - FresnelC[(-b + 2 c s - c v + 2 (-d + 2 f s - f v) Sqrt[z])/ (Sqrt[2 Pi] Sqrt[I (-d + 2 f s - f v)])] Sinh[e - 2 g s + g v + (b + c (-2 s + v))^2/(-4 d + 8 f s - 4 f v)]))/(I (-d + 2 f s - f v))^(3/2)), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

 Standard Form

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SqrtBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]]]], ")"]]]]]]]], "]"]]]], "-", RowBox[List[RowBox[List["FresnelC", "[", FractionBox[RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]]]], ")"]]]]]]]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["e", "-", RowBox[List["2", " ", "g", " ", "s"]], "+", RowBox[List["g", " ", "v"]], "+", FractionBox[SuperscriptBox[RowBox[List["(", 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 MathML Form

 sinh ( z b + e + d z ) cosh v ( z c + g + f z ) z 2 - v - 1 s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 ( ( - d - 2 f s + f v ) ) 3 / 2 ( - 2 ( - d - 2 f s + f v ) cosh ( e + 2 g s - g v - ( - d - 2 f s + f v ) z - ( - b - 2 c s + c v ) z ) - 2 π ( - b - 2 c s + c v ) ( cosh ( ( - b - 2 c s + c v ) 2 - 4 d - 8 f s + 4 f v + e + 2 g s - g v ) S TagBox["S", FresnelS] ( - b - 2 c s + c v + 2 ( - d - 2 f s + f v ) z 2 π ( - d - 2 f s + f v ) ) - C TagBox["C", FresnelC] ( - b - 2 c s + c v + 2 ( - d - 2 f s + f v ) z 2 π ( - d - 2 f s + f v ) ) sinh ( ( - b - 2 c s + c v ) 2 - 4 d - 8 f s + 4 f v + e + 2 g s - g v ) ) ) + 1 ( ( - d + 2 f s - f v ) ) 3 / 2 ( - 2 ( - d + 2 f s - f v ) cosh ( e - 2 g s + g v - ( - d + 2 f s - f v ) z - ( - b + 2 c s - c v ) z ) - 2 π ( - b + 2 c s - c v ) ( cosh ( ( b + c ( v - 2 s ) ) 2 - 4 d + 8 f s - 4 f v + e - 2 g s + g v ) S TagBox["S", FresnelS] ( - b + 2 c s - c v + 2 ( - d + 2 f s - f v ) z 2 π ( - d + 2 f s - f v ) ) - C TagBox["C", FresnelC] ( - b + 2 c s - c v + 2 ( - d + 2 f s - f v ) z 2 π ( - d + 2 f s - f v ) ) sinh ( ( b + c ( v - 2 s ) ) 2 - 4 d + 8 f s - 4 f v + e - 2 g s + g v ) ) ) ) - 1 ( - d ) 3 / 2 ( 2 - v - 1 ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) ( 2 - d cosh ( z b + e + d z ) - b 2 π ( cosh ( b 2 4 d - e ) S TagBox["S", FresnelS] ( - b - 2 d z - d 2 π ) + C TagBox["C", FresnelC] ( - b - 2 d z - d 2 π ) sinh ( b 2 4 d - e ) ) ) ) /; m + v + Condition z z 1 2 b e d z z 1 2 c g f z v 2 -1 v -1 s 0 v -1 2 -1 Binomial v s 1 -1 d -1 2 f s f v 3 2 -1 -2 -1 d -1 2 f s f v 1 2 e 2 g s -1 g v -1 -1 d -1 2 f s f v z -1 -1 b -1 2 c s c v z 1 2 -1 2 1 2 -1 b -1 2 c s c v -1 b -1 2 c s c v 2 -4 d -1 8 f s 4 f v -1 e 2 g s -1 g v FresnelS -1 b -1 2 c s c v 2 -1 d -1 2 f s f v z 1 2 2 1 2 -1 d -1 2 f s f v 1 2 -1 -1 FresnelC -1 b -1 2 c s c v 2 -1 d -1 2 f s f v z 1 2 2 1 2 -1 d -1 2 f s f v 1 2 -1 -1 b -1 2 c s c v 2 -4 d -1 8 f s 4 f v -1 e 2 g s -1 g v 1 -1 d 2 f s -1 f v 3 2 -1 -2 -1 d 2 f s -1 f v 1 2 e -1 2 g s g v -1 -1 d 2 f s -1 f v z -1 -1 b 2 c s -1 c v z 1 2 -1 2 1 2 -1 b 2 c s -1 c v b c v -1 2 s 2 -4 d 8 f s -1 4 f v -1 e -1 2 g s g v FresnelS -1 b 2 c s -1 c v 2 -1 d 2 f s -1 f v z 1 2 2 1 2 -1 d 2 f s -1 f v 1 2 -1 -1 FresnelC -1 b 2 c s -1 c v 2 -1 d 2 f s -1 f v z 1 2 2 1 2 -1 d 2 f s -1 f v 1 2 -1 b c v -1 2 s 2 -4 d 8 f s -1 4 f v -1 e -1 2 g s g v -1 1 -1 d 3 2 -1 2 -1 v -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 d 1 2 z 1 2 b e d z -1 b 2 1 2 b 2 4 d -1 -1 e FresnelS -1 b -1 2 d z 1 2 -1 d 1 2 2 1 2 -1 FresnelC -1 b -1 2 d z 1 2 -1 d 1 2 2 1 2 -1 b 2 4 d -1 -1 e m SuperPlus v SuperPlus [/itex]

 Rule Form

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

 2002-12-18