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/01.20.21.4655.01

 Input Form

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

 Standard Form

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 MathML Form

 p z sinh m ( b z ) cosh v ( c z 2 ) z m 2 - m - v p z ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 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 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) p - 1 c ( ( m 2 - m - v - 1 π ) ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) s = 0 v - 1 2 1 v - 2 s ( ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( p 2 4 c ( v - 2 s ) - c ( v - 2 s ) erfi ( p - 2 c ( v - 2 s ) z 2 - c ( v - 2 s ) ) - - p 2 4 c ( v - 2 s ) c ( v - 2 s ) erfi ( p + 2 c ( v - 2 s ) z 2 c ( v - 2 s ) ) ) ) ) + m 2 - m - v + 1 ( 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 ) k = 0 m - 1 2 ( - 1 ) k p z ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( p cos ( π m 2 + b ( m - 2 k ) z ) + b ( m - 2 k ) sin ( π m 2 + b ( m - 2 k ) z ) ) ( p - b ( m - 2 k ) ) ( b ( m - 2 k ) + p ) - 1 c ( ( m 2 - m - v - 1 π ) k = 0 m - 1 2 ( - 1 ) k ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] s = 0 v - 1 2 1 v - 2 s ( ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( p - b ( 2 k - m ) ) 2 - 2 c m π ( v - 2 s ) 4 c ( v - 2 s ) - c ( v - 2 s ) erfi ( - b ( 2 k - m ) + p - 2 c ( v - 2 s ) z 2 - c ( v - 2 s ) ) + ( p - b ( m - 2 k ) ) 2 + 2 c m π ( v - 2 s ) 4 c ( v - 2 s ) - c ( v - 2 s ) erfi ( - b ( m - 2 k ) + p - 2 c ( v - 2 s ) z 2 - c ( v - 2 s ) ) - - ( b ( 2 k - m ) + p ) 2 - 2 c m π ( v - 2 s ) 4 c ( v - 2 s ) c ( v - 2 s ) erfi ( b ( 2 k - m ) + p + 2 c ( v - 2 s ) z 2 c ( v - 2 s ) ) - - ( b ( m - 2 k ) + p ) 2 + 2 c m π ( v - 2 s ) 4 c ( v - 2 s ) c ( v - 2 s ) erfi ( b ( m - 2 k ) + p + 2 c ( v - 2 s ) z 2 c ( v - 2 s ) ) ) ) ) /; m + v + Condition z p z b z m c z 2 v m 2 -1 m -1 v p z Binomial m m 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 p -1 -1 1 c -1 m 2 -1 m -1 v -1 1 2 Binomial m m 2 -1 1 -1 \$CellContext`m 2 s 0 v -1 2 -1 1 v -1 2 s -1 Binomial v s p 2 4 c v -1 2 s -1 -1 c v -1 2 s 1 2 Erfi p -1 2 c v -1 2 s z 2 -1 c v -1 2 s 1 2 -1 -1 -1 p 2 4 c v -1 2 s -1 c v -1 2 s 1 2 Erfi p 2 c v -1 2 s z 2 c v -1 2 s 1 2 -1 m 2 -1 m -1 v 1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 k 0 m -1 2 -1 -1 k p z Binomial m k p m 2 -1 b m -1 2 k z b m -1 2 k m 2 -1 b m -1 2 k z p -1 b m -1 2 k b m -1 2 k p -1 -1 1 c -1 m 2 -1 m -1 v -1 1 2 k 0 m -1 2 -1 -1 k Binomial m k s 0 v -1 2 -1 1 v -1 2 s -1 Binomial v s p -1 b 2 k -1 m 2 -1 2 c m v -1 2 s 4 c v -1 2 s -1 -1 c v -1 2 s 1 2 Erfi -1 b 2 k -1 m p -1 2 c v -1 2 s z 2 -1 c v -1 2 s 1 2 -1 p -1 b m -1 2 k 2 2 c m v -1 2 s 4 c v -1 2 s -1 -1 c v -1 2 s 1 2 Erfi -1 b m -1 2 k p -1 2 c v -1 2 s z 2 -1 c v -1 2 s 1 2 -1 -1 -1 b 2 k -1 m p 2 -1 2 c m v -1 2 s 4 c v -1 2 s -1 c v -1 2 s 1 2 Erfi b 2 k -1 m p 2 c v -1 2 s z 2 c v -1 2 s 1 2 -1 -1 -1 b m -1 2 k p 2 2 c m v -1 2 s 4 c v -1 2 s -1 c v -1 2 s 1 2 Erfi b m -1 2 k p 2 c v -1 2 s z 2 c v -1 2 s 1 2 -1 m SuperPlus v SuperPlus [/itex]

 Rule Form

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

 2002-12-18