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/01.20.21.3970.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18