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/01.20.21.4111.01

 Input Form

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

 Standard Form

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"+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 sinh ( b z 2 + d z + e ) cosh v ( c z 2 + f z + g ) z 2 - v - 2 π 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]]]]] ( - ( d - 2 f s + f v ) 2 - 4 b + 8 c s - 4 c v - e + g ( 2 s - v ) - b + 2 c s - c v erfi ( - d - 2 b z + ( 2 s - v ) ( f + 2 c z ) 2 - b + 2 c s - c v ) b + c ( v - 2 s ) + 1 b + 2 c s - c v ( - ( f ( v - 2 s ) - d ) 2 - 4 b - 8 c s + 4 c v - e + g ( v - 2 s ) ( - b - 2 c s + c v erfi ( - d - 2 b z - ( 2 s - v ) ( f + 2 c z ) 2 - b - 2 c s + c v ) + 2 ( ( - d - 2 f s + f v ) 2 - 4 b - 8 c s + 4 c v + e + g ( 2 s - v ) ) b + 2 c s - c v erfi ( d + 2 b z + ( 2 s - v ) ( f + 2 c z ) 2 b + 2 c s - c v ) ) ) + ( d - 2 f s + f v ) 2 - 4 b + 8 c s - 4 c v + e + g ( v - 2 s ) erfi ( d + 2 b z - ( 2 s - v ) ( f + 2 c z ) 2 b + c ( v - 2 s ) ) b + c ( v - 2 s ) ) - 1 b ( 2 - v - 2 - d 2 4 b - e 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]]]]] ( - b 2 e erfi ( d + 2 b z 2 b ) - - b d 2 2 b erfi ( - b ( d + 2 b z ) 2 b ) ) ( 1 - v mod 2 \$CellContext`v 2 ) ) /; v + Condition z b z 2 d z e c z 2 f z g v 2 -1 v -2 1 2 s 0 v -1 2 -1 Binomial v s -1 d -1 2 f s f v 2 -4 b 8 c s -1 4 c v -1 -1 e g 2 s -1 v -1 b 2 c s -1 c v 1 2 Erfi -1 d -1 2 b z 2 s -1 v f 2 c z 2 -1 b 2 c s -1 c v 1 2 -1 b c v -1 2 s -1 1 b 2 c s -1 c v -1 -1 f v -1 2 s -1 d 2 -4 b -1 8 c s 4 c v -1 -1 e g v -1 2 s -1 b -1 2 c s c v 1 2 Erfi -1 d -1 2 b z -1 2 s -1 v f 2 c z 2 -1 b -1 2 c s c v 1 2 -1 2 -1 d -1 2 f s f v 2 -4 b -1 8 c s 4 c v -1 e g 2 s -1 v b 2 c s -1 c v 1 2 Erfi d 2 b z 2 s -1 v f 2 c z 2 b 2 c s -1 c v 1 2 -1 d -1 2 f s f v 2 -4 b 8 c s -1 4 c v -1 e g v -1 2 s Erfi d 2 b z -1 2 s -1 v f 2 c z 2 b c v -1 2 s 1 2 -1 b c v -1 2 s 1 2 -1 -1 1 b -1 2 -1 v -2 -1 d 2 4 b -1 -1 e 1 2 Binomial v v 2 -1 -1 b 1 2 2 e Erfi d 2 b z 2 b 1 2 -1 -1 -1 b 1 2 d 2 2 b -1 Erfi -1 b 1 2 d 2 b z 2 b -1 1 -1 \$CellContext`v 2 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18