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/01.20.21.4642.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18