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/01.20.21.0821.01

 Input Form

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

 Standard Form

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RowBox[List["2", " ", "\[ImaginaryI]", " ", "e", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "e", " ", "m"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "c"]], "+", RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "d", " ", "k"]], "-", RowBox[List["d", " ", "m"]]]], ")"]], " ", "z"]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18