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/01.20.21.1557.01

 Input Form

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

 Standard Form

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RowBox[List["2", " ", SqrtBox[RowBox[List["c", "+", RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]]]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18