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/01.20.21.3968.01

 Input Form

 Integrate[z^(\[Alpha] - 1) E^(p z) Cos[c z] Cosh[b + a z]^v, z] == (-2^(-1 - v)) z^\[Alpha] Binomial[v, v/2] (Gamma[\[Alpha], ((-I) c - p) z]/(((-I) c - p) z)^\[Alpha] + Gamma[\[Alpha], (I c - p) z]/((I c - p) z)^\[Alpha]) (1 - Mod[v, 2]) - 2^(-1 - v) z^\[Alpha] Sum[E^(-2 b k - b v) Binomial[v, k] (E^(2 b v) (Gamma[\[Alpha], ((-I) c + 2 a k - p - a v) z]/ (((-I) c + 2 a k - p - a v) z)^\[Alpha] + Gamma[\[Alpha], (I c + 2 a k - p - a v) z]/ ((I c + 2 a k - p - a v) z)^\[Alpha]) + (E^(4 b k) Gamma[\[Alpha], ((-I) c - 2 a k - p + a v) z])/ (((-I) c - 2 a k - p + a v) z)^\[Alpha] + (E^(4 b k) Gamma[\[Alpha], (I c - 2 a k - p + a v) z])/ ((I c - 2 a k - p + a v) z)^\[Alpha]), {k, 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 ) cosh v ( b + a z ) z - 2 - v - 1 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]]]]] ( Γ ( α , ( - c - p ) z ) ( ( - c - p ) z ) - α + ( ( c - p ) z ) - α Γ ( α , ( c - p ) z ) ) ( 1 - v mod 2 \$CellContext`v 2 ) - 2 - v - 1 z α 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 , ( - c - 2 a k - p + a v ) z ) ( ( - c - 2 a k - p + a v ) z ) - α + 4 b k ( ( c - 2 a k - p + a v ) z ) - α Γ ( α , ( c - 2 a k - p + a v ) z ) + 2 b v ( Γ ( α , ( - c + 2 a k - p - a v ) z ) ( ( - c + 2 a k - p - a v ) z ) - α + ( ( c + 2 a k - p - a v ) z ) - α Γ ( α , ( c + 2 a k - p - a v ) z ) ) ) /; v + Condition z z α -1 p z c z b a z v -1 2 -1 v -1 z α Binomial v v 2 -1 Gamma α -1 c -1 p z -1 c -1 p z -1 α c -1 p z -1 α Gamma α c -1 p z 1 -1 \$CellContext`v 2 -1 2 -1 v -1 z α k 0 v -1 2 -1 -2 b k -1 b v Binomial v k 4 b k Gamma α -1 c -1 2 a k -1 p a v z -1 c -1 2 a k -1 p a v z -1 α 4 b k c -1 2 a k -1 p a v z -1 α Gamma α c -1 2 a k -1 p a v z 2 b v Gamma α -1 c 2 a k -1 p -1 a v z -1 c 2 a k -1 p -1 a v z -1 α c 2 a k -1 p -1 a v z -1 α Gamma α c 2 a k -1 p -1 a v z v SuperPlus [/itex]

 Rule Form

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

 2002-12-18