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/01.20.21.3853.01

 Input Form

 Integrate[E^(b z^r + e) Cos[a z^r + q]^m Cosh[c z^r + g]^v, z] == (-((2^(-m - v) z)/r)) ((E^e Binomial[m, m/2] Binomial[v, v/2] Gamma[1/r, (-b) z^r] (1 - Mod[m, 2]) (1 - Mod[v, 2]))/ ((-b) z^r)^r^(-1) + Binomial[v, v/2] (1 - Mod[v, 2]) Sum[Binomial[m, k] ((E^(e - 2 I k q + I m q) Gamma[1/r, (-b + 2 I a k - I a m) z^r])/((-b + 2 I a k - I a m) z^r)^r^(-1) + (E^(e + 2 I k q - I m q) Gamma[1/r, (-b - 2 I a k + I a m) z^r])/ ((-b - 2 I a k + I a m) z^r)^r^(-1)), {k, 0, Floor[(1/2) (-1 + m)]}] + Binomial[m, m/2] (1 - Mod[m, 2]) Sum[Binomial[v, s] ((E^(e - 2 g s + g v) Gamma[1/r, (-b + 2 c s - c v) z^r])/((-b + 2 c s - c v) z^r)^r^(-1) + (E^(e + 2 g s - g v) Gamma[1/r, (-b - 2 c s + c v) z^r])/ ((-b - 2 c s + c v) z^r)^r^(-1)), {s, 0, Floor[(1/2) (-1 + v)]}] + Sum[Binomial[m, k] Sum[Binomial[v, s] ((E^(e - 2 I k q + I m q - 2 g s + g v) Gamma[1/r, (-b + 2 I a k - I a m + 2 c s - c v) z^r])/ ((-b + 2 I a k - I a m + 2 c s - c v) z^r)^r^(-1) + (E^(e + 2 I k q - I m q - 2 g s + g v) Gamma[1/r, (-b - 2 I a k + I a m + 2 c s - c v) z^r])/ ((-b - 2 I a k + I a m + 2 c s - c v) z^r)^r^(-1) + (E^(e - 2 I k q + I m q + 2 g s - g v) Gamma[1/r, (-b + 2 I a k - I a m - 2 c s + c v) z^r])/ ((-b + 2 I a k - I a m - 2 c s + c v) z^r)^r^(-1) + (E^(e + 2 I k q - I m q + 2 g s - g v) Gamma[1/r, (-b - 2 I a k + I a m - 2 c s + c v) z^r])/ ((-b - 2 I a k + I a m - 2 c s + c v) z^r)^r^(-1)), {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

 b z r + e cos m ( a z r + q ) cosh v ( c z r + g ) z - 2 - m - v z r ( e ( 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 ( 1 r , - b z r ) ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) ( - b z r ) - 1 / r + ( 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 ) 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]]]]] ( e + 2 k q - m q Γ ( 1 r , ( - b - 2 a k + a m ) z r ) ( ( - b - 2 a k + a m ) z r ) - 1 / r + e - 2 k q + m q ( ( - b + 2 a k - a m ) z r ) - 1 / r Γ ( 1 r , ( - b + 2 a k - a m ) z r ) ) + ( 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 ) 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]]]]] ( e + 2 g s - g v Γ ( 1 r , ( - b - 2 c s + c v ) z r ) ( ( - b - 2 c s + c v ) z r ) - 1 / r + e - 2 g s + g v ( ( - b + 2 c s - c v ) z r ) - 1 / r Γ ( 1 r , ( - b + 2 c s - c v ) z r ) ) + 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 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( e + 2 k q - m q + 2 g s - g v Γ ( 1 r , ( - b - 2 a k + a m - 2 c s + c v ) z r ) ( ( - b - 2 a k + a m - 2 c s + c v ) z r ) - 1 / r + e - 2 k q + m q + 2 g s - g v ( ( - b + 2 a k - a m - 2 c s + c v ) z r ) - 1 / r Γ ( 1 r , ( - b + 2 a k - a m - 2 c s + c v ) z r ) + e + 2 k q - m q - 2 g s + g v ( ( - b - 2 a k + a m + 2 c s - c v ) z r ) - 1 / r Γ ( 1 r , ( - b - 2 a k + a m + 2 c s - c v ) z r ) + e - 2 k q + m q - 2 g s + g v ( ( - b + 2 a k - a m + 2 c s - c v ) z r ) - 1 / r Γ ( 1 r , ( - b + 2 a k - a m + 2 c s - c v ) z r ) ) ) /; m + v + Condition z b z r e a z r q m c z r g v -1 2 -1 m -1 v z r -1 e Binomial m m 2 -1 Binomial v v 2 -1 Gamma 1 r -1 -1 b z r 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 -1 b z r -1 r -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 k 0 m -1 2 -1 Binomial m k e 2 k q -1 m q Gamma 1 r -1 -1 b -1 2 a k a m z r -1 b -1 2 a k a m z r -1 r -1 e -1 2 k q m q -1 b 2 a k -1 a m z r -1 r -1 Gamma 1 r -1 -1 b 2 a k -1 a m z r Binomial m m 2 -1 1 -1 \$CellContext`m 2 s 0 v -1 2 -1 Binomial v s e 2 g s -1 g v Gamma 1 r -1 -1 b -1 2 c s c v z r -1 b -1 2 c s c v z r -1 r -1 e -1 2 g s g v -1 b 2 c s -1 c v z r -1 r -1 Gamma 1 r -1 -1 b 2 c s -1 c v z r k 0 m -1 2 -1 Binomial m k s 0 v -1 2 -1 Binomial v s e 2 k q -1 m q 2 g s -1 g v Gamma 1 r -1 -1 b -1 2 a k a m -1 2 c s c v z r -1 b -1 2 a k a m -1 2 c s c v z r -1 r -1 e -1 2 k q m q 2 g s -1 g v -1 b 2 a k -1 a m -1 2 c s c v z r -1 r -1 Gamma 1 r -1 -1 b 2 a k -1 a m -1 2 c s c v z r e 2 k q -1 m q -1 2 g s g v -1 b -1 2 a k a m 2 c s -1 c v z r -1 r -1 Gamma 1 r -1 -1 b -1 2 a k a m 2 c s -1 c v z r e -1 2 k q m q -1 2 g s g v -1 b 2 a k -1 a m 2 c s -1 c v z r -1 r -1 Gamma 1 r -1 -1 b 2 a k -1 a m 2 c s -1 c v z r m SuperPlus v SuperPlus [/itex]

 Rule Form

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

 2002-12-18