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/01.20.21.4837.01

 Input Form

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

 z α - 1 p z sinh m ( d + c z ) cosh v ( b + a z ) z - 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]]]]] ( 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 ) z α ( - p z ) - α Γ ( α , - p z ) - 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 ) z α 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 ) ) - 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 ) z α 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]]]]] - d ( 2 k + m ) ( 2 d m E TagBox["E", ExpIntegralE] 1 - α ( ( 2 c k - c m - p ) z ) + 4 d k + m π E TagBox["E", ExpIntegralE] 1 - α ( - ( 2 c k - c m + p ) z ) ) - 2 - m - v z α 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 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] - 2 d k - d m - 2 b s - b v ( 2 d m ( 4 b s E TagBox["E", ExpIntegralE] 1 - α ( ( 2 c k - c m - 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 ) ) + 4 d k + m π ( 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 -1 m 2 -1 m -1 v Binomial m m 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 z α -1 p z -1 α Gamma α -1 p z -1 m 2 -1 m -1 v Binomial m m 2 -1 1 -1 \$CellContext`m 2 z α 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 2 -1 m -1 v Binomial v v 2 -1 1 -1 \$CellContext`v 2 z α k 0 m -1 2 -1 -1 k Binomial m k -1 d 2 k m 2 d m ExpIntegralE 1 -1 α 2 c k -1 c m -1 p z 4 d k m ExpIntegralE 1 -1 α -1 2 c k -1 c m p z -1 2 -1 m -1 v z α s 0 v -1 2 -1 Binomial v s k 0 m -1 2 -1 -1 k Binomial m k -2 d k -1 d m -1 2 b s -1 b v 2 d m 4 b s ExpIntegralE 1 -1 α 2 c k -1 c m -1 p -1 2 a s a v z 2 b v ExpIntegralE 1 -1 α 2 c k -1 c m -1 p 2 a s -1 a v z 4 d k m 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 -1 2 c k -1 c m p -1 2 a s 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