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/01.20.21.4110.01

 Input Form

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

 Standard Form

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 MathML Form

 sinh ( b z 2 + d z + e ) cosh v ( c z 2 + f z + g ) z - 2 - v - 1 2 π ( ( 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 ) ( C TagBox["C", FresnelC] ( d + 2 b z b 2 π ) sinh ( d 2 4 b - e ) - cosh ( d 2 4 b - e ) S TagBox["S", FresnelS] ( d + 2 b z b 2 π ) ) b + 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 ( - b - 2 c s + c v ) ( cosh ( ( - d - 2 f s + f v ) 2 - 4 b - 8 c s + 4 c v + e + 2 g s - g v ) S TagBox["S", FresnelS] ( - d - 2 f s + f v + 2 ( - b - 2 c s + c v ) z 2 π ( - b - 2 c s + c v ) ) - C TagBox["C", FresnelC] ( - d - 2 f s + f v + 2 ( - b - 2 c s + c v ) z 2 π ( - b - 2 c s + c v ) ) sinh ( ( - d - 2 f s + f v ) 2 - 4 b - 8 c s + 4 c v + e + 2 g s - g v ) ) + 1 - b + 2 c s - c v ( cosh ( ( d + f ( v - 2 s ) ) 2 - 4 b + 8 c s - 4 c v + e - 2 g s + g v ) S TagBox["S", FresnelS] ( - d - 2 b z + ( 2 s - v ) ( f + 2 c z ) 2 π ( - b + 2 c s - c v ) ) - C TagBox["C", FresnelC] ( - d - 2 b z + ( 2 s - v ) ( f + 2 c z ) 2 π ( - b + 2 c s - c v ) ) sinh ( ( d + f ( v - 2 s ) ) 2 - 4 b + 8 c s - 4 c v + e - 2 g s + g v ) ) ) ) /; v + Condition z b z 2 d z e c z 2 f z g v -1 2 -1 v -1 1 2 1 2 Binomial v v 2 -1 1 -1 \$CellContext`v 2 FresnelC d 2 b z b 1 2 2 1 2 -1 d 2 4 b -1 -1 e -1 d 2 4 b -1 -1 e FresnelS d 2 b z b 1 2 2 1 2 -1 b 1 2 -1 s 0 v -1 2 -1 Binomial v s 1 -1 b -1 2 c s c v 1 2 -1 -1 d -1 2 f s f v 2 -4 b -1 8 c s 4 c v -1 e 2 g s -1 g v FresnelS -1 d -1 2 f s f v 2 -1 b -1 2 c s c v z 2 1 2 -1 b -1 2 c s c v 1 2 -1 -1 FresnelC -1 d -1 2 f s f v 2 -1 b -1 2 c s c v z 2 1 2 -1 b -1 2 c s c v 1 2 -1 -1 d -1 2 f s f v 2 -4 b -1 8 c s 4 c v -1 e 2 g s -1 g v 1 -1 b 2 c s -1 c v 1 2 -1 d f v -1 2 s 2 -4 b 8 c s -1 4 c v -1 e -1 2 g s g v FresnelS -1 d -1 2 b z 2 s -1 v f 2 c z 2 1 2 -1 b 2 c s -1 c v 1 2 -1 -1 FresnelC -1 d -1 2 b z 2 s -1 v f 2 c z 2 1 2 -1 b 2 c s -1 c v 1 2 -1 d f v -1 2 s 2 -4 b 8 c s -1 4 c v -1 e -1 2 g s g v v SuperPlus [/itex]

 Rule Form

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

 2002-12-18