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/01.20.21.3998.01

 Input Form

 Integrate[z^(\[Alpha] - 1) E^(p z) Cos[c z]^m Cosh[b + a z]^v, z] == ((-2^(-m - v)) z^\[Alpha] Binomial[m, m/2] Binomial[v, v/2] Gamma[\[Alpha], (-p) z] (1 - Mod[m, 2]) (1 - Mod[v, 2]))/ ((-p) z)^\[Alpha] - 2^(-m - v) z^\[Alpha] Binomial[v, v/2] (1 - Mod[v, 2]) Sum[Binomial[m, s] (Gamma[\[Alpha], (-p - I c (m - 2 s)) z]/((-p - I c (m - 2 s)) z)^ \[Alpha] + Gamma[\[Alpha], (I c m - p - 2 I c s) z]/ ((I c m - p - 2 I c s) z)^\[Alpha]), {s, 0, Floor[(1/2) (-1 + m)]}] - 2^(-m - v) z^\[Alpha] Binomial[m, m/2] (1 - Mod[m, 2]) Sum[E^(-2 b k - b v) Binomial[v, k] ((E^(4 b k) Gamma[\[Alpha], (-2 a k - p + a v) z])/ ((-2 a k - p + a v) z)^\[Alpha] + (E^(2 b v) Gamma[\[Alpha], (-p - a (-2 k + v)) z])/ ((-p - a (-2 k + v)) z)^\[Alpha]), {k, 0, Floor[(1/2) (-1 + v)]}] - 2^(-m - v) z^\[Alpha] Sum[Binomial[v, k] Sum[E^(-2 b k - b v) Binomial[m, s] (E^(2 b v) (Gamma[\[Alpha], (2 a k + I c m - p - 2 I c s - a v) z]/ ((2 a k + I c m - p - 2 I c s - a v) z)^\[Alpha] + Gamma[\[Alpha], (2 a k - I c m - p + 2 I c s - a v) z]/ ((2 a k - I c m - p + 2 I c s - a v) z)^\[Alpha]) + (E^(4 b k) Gamma[\[Alpha], (-2 a k + I c m - p - 2 I c s + a v) z])/ ((-2 a k + I c m - p - 2 I c s + a v) z)^\[Alpha] + (E^(4 b k) Gamma[\[Alpha], (-2 a k - I c m - p + 2 I c s + a v) z])/ ((-2 a k - I c m - p + 2 I c s + a v) z)^\[Alpha]), {s, 0, Floor[(1/2) (-1 + m)]}], {k, 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 cos m ( 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]]]]] Γ ( α , - p z ) ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) ( - p z ) - α - 2 - m - v z α ( 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 ) s = 0 m - 1 2 ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( Γ ( α , ( c m - p - 2 c s ) z ) ( ( c m - p - 2 c s ) z ) - α + ( ( - p - c ( m - 2 s ) ) z ) - α Γ ( α , ( - p - c ( m - 2 s ) ) 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]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) k = 0 v - 1 2 - 2 b k - b v ( v k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 4 b k Γ ( α , ( - 2 a k - p + a v ) z ) ( ( - 2 a k - p + a v ) z ) - α + 2 b v ( ( - p - a ( v - 2 k ) ) z ) - α Γ ( α , ( - p - a ( v - 2 k ) ) z ) ) - 2 - m - v z α k = 0 v - 1 2 ( v k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] s = 0 m - 1 2 - 2 b k - b v ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 4 b k Γ ( α , ( - 2 a k - c m - p + 2 c s + a v ) z ) ( ( - 2 a k - c m - p + 2 c s + a v ) z ) - α + 4 b k ( ( - 2 a k + c m - p - 2 c s + a v ) z ) - α Γ ( α , ( - 2 a k + c m - p - 2 c s + a v ) z ) + 2 b v ( Γ ( α , ( 2 a k - c m - p + 2 c s - a v ) z ) ( ( 2 a k - c m - p + 2 c s - a v ) z ) - α + ( ( 2 a k + c m - p - 2 c s - a v ) z ) - α Γ ( α , ( 2 a k + c m - p - 2 c s - a v ) z ) ) ) /; m + v + Condition z z α -1 p z c z m b a z v -1 2 -1 m -1 v z α Binomial m m 2 -1 Binomial v v 2 -1 Gamma α -1 p z 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 -1 p z -1 α -1 2 -1 m -1 v z α Binomial v v 2 -1 1 -1 \$CellContext`v 2 s 0 m -1 2 -1 Binomial m s Gamma α c m -1 p -1 2 c s z c m -1 p -1 2 c s z -1 α -1 p -1 c m -1 2 s z -1 α Gamma α -1 p -1 c m -1 2 s z -1 2 -1 m -1 v z α Binomial m m 2 -1 1 -1 \$CellContext`m 2 k 0 v -1 2 -1 -2 b k -1 b v Binomial v k 4 b k Gamma α -2 a k -1 p a v z -2 a k -1 p a v z -1 α 2 b v -1 p -1 a v -1 2 k z -1 α Gamma α -1 p -1 a v -1 2 k z -1 2 -1 m -1 v z α k 0 v -1 2 -1 Binomial v k s 0 m -1 2 -1 -2 b k -1 b v Binomial m s 4 b k Gamma α -2 a k -1 c m -1 p 2 c s a v z -2 a k -1 c m -1 p 2 c s a v z -1 α 4 b k -2 a k c m -1 p -1 2 c s a v z -1 α Gamma α -2 a k c m -1 p -1 2 c s a v z 2 b v Gamma α 2 a k -1 c m -1 p 2 c s -1 a v z 2 a k -1 c m -1 p 2 c s -1 a v z -1 α 2 a k c m -1 p -1 2 c s -1 a v z -1 α Gamma α 2 a k c m -1 p -1 2 c 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