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/01.20.21.4087.01

 Input Form

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

 Standard Form

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RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "d"]]]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox["d", RowBox[List["3", "/", "2"]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", "d"]]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["e", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["d"]]]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 sinh ( z b + e + d z ) cosh v ( z c + g ) z 2 - v - 2 ( 4 e cosh ( z b + e + d z ) d + b b 2 4 d π erfi ( b + 2 d z 2 - d ) ( - d ) 3 / 2 - b 2 e - b 2 4 d π erfi ( b + 2 d z 2 d ) d 3 / 2 ) - e ( 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 - v - 2 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]]]]] ( e - g ( v - 2 s ) ( 4 g ( v - 2 s ) - e cosh ( e + 2 g s - g v + d z + ( b + 2 c s - c v ) z ) d + ( c ( v - 2 s ) - b ) 2 4 d + 2 ( g ( v - 2 s ) - e ) π ( c ( v - 2 s ) - b ) erfi ( - b + c ( v - 2 s ) - 2 d z 2 - d ) ( - d ) 3 / 2 - - ( b - c ( v - 2 s ) ) 2 4 d π ( c ( v - 2 s ) - b ) erfi ( - b + c ( v - 2 s ) - 2 d z 2 d ) d 3 / 2 ) - - e - g ( v - 2 s ) ( - 4 e + g ( v - 2 s ) cosh ( e + g ( v - 2 s ) + d z + ( b - 2 c s + c v ) z ) d - ( - b - c ( v - 2 s ) ) 2 4 d π ( b + c ( v - 2 s ) ) erfi ( b + c ( v - 2 s ) + 2 d z 2 - d ) ( - d ) 3 / 2 + 2 ( e + g ( v - 2 s ) ) - ( b + c ( v - 2 s ) ) 2 4 d π ( b + c ( v - 2 s ) ) erfi ( b + c ( v - 2 s ) + 2 d z 2 d ) d 3 / 2 ) ) /; v + Condition z z 1 2 b e d z z 1 2 c g v 2 -1 v -2 4 e z 1 2 b e d z d -1 b b 2 4 d -1 1 2 Erfi b 2 d z 1 2 2 -1 d 1 2 -1 -1 d 3 2 -1 -1 b 2 e -1 b 2 4 d -1 1 2 Erfi b 2 d z 1 2 2 d 1 2 -1 d 3 2 -1 -1 e Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 s 0 v -1 2 -1 Binomial v s e -1 g v -1 2 s 4 g v -1 2 s -1 e e 2 g s -1 g v d z b 2 c s -1 c v z 1 2 d -1 c v -1 2 s -1 b 2 4 d -1 2 g v -1 2 s -1 e 1 2 c v -1 2 s -1 b Erfi -1 b c v -1 2 s -1 2 d z 1 2 2 -1 d 1 2 -1 -1 d 3 2 -1 -1 -1 b -1 c v -1 2 s 2 4 d -1 1 2 c v -1 2 s -1 b Erfi -1 b c v -1 2 s -1 2 d z 1 2 2 d 1 2 -1 d 3 2 -1 -1 -1 e -1 g v -1 2 s -1 4 e g v -1 2 s e g v -1 2 s d z b -1 2 c s c v z 1 2 d -1 -1 -1 b -1 c v -1 2 s 2 4 d -1 1 2 b c v -1 2 s Erfi b c v -1 2 s 2 d z 1 2 2 -1 d 1 2 -1 -1 d 3 2 -1 2 e g v -1 2 s -1 b c v -1 2 s 2 4 d -1 1 2 b c v -1 2 s Erfi b c v -1 2 s 2 d z 1 2 2 d 1 2 -1 d 3 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18