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/01.20.21.4001.01

 Input Form

 Integrate[z^(\[Alpha] - 1) E^(p z) Cos[d + c z]^m Cosh[b + a z]^v, z] == 2^(-m - v) z^\[Alpha] ((-Binomial[m, m/2]) Binomial[v, v/2] ExpIntegralE[1 - \[Alpha], (-p) z] (-1 + Mod[m, 2]) (-1 + Mod[v, 2]) + Binomial[v, v/2] (-1 + Mod[v, 2]) Sum[(Binomial[m, s] (ExpIntegralE[1 - \[Alpha], (-p + I c (m - 2 s)) z] + E^(2 I d (m - 2 s)) ExpIntegralE[1 - \[Alpha], (-(p + I c (m - 2 s))) z]))/E^(I d (m - 2 s)), {s, 0, Floor[(1/2) (-1 + m)]}] + Binomial[m, m/2] (-1 + Mod[m, 2]) Sum[(Binomial[v, s] (E^(4 b s) ExpIntegralE[1 - \[Alpha], (-(p + 2 a s - a v)) z] + E^(2 b v) ExpIntegralE[1 - \[Alpha], (-(p + a (-2 s + v))) z]))/E^(b (2 s + v)), {s, 0, Floor[(1/2) (-1 + v)]}] - Sum[Binomial[m, k] Sum[E^((-I) d (2 k + m) - b (2 s + v)) Binomial[v, s] (E^(2 I d m) (E^(2 b v) ExpIntegralE[1 - \[Alpha], (I c (2 k - m) - p + 2 a s - a v) z] + E^(4 b s) ExpIntegralE[1 - \[Alpha], (I c (2 k - m) - p - 2 a s + a v) z]) + E^(4 I d k) (E^(2 b v) ExpIntegralE[1 - \[Alpha], (-2 I c k + I c m - p + 2 a s - a v) z] + E^(4 b s) ExpIntegralE[1 - \[Alpha], (I c (-2 k + m) - p - 2 a s + a v) z])), {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

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

 Rule Form

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

 2002-12-18