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/01.20.21.3850.01

 Input Form

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

 p z r cos m ( b z r ) cosh v ( c z r ) z - 2 - m - v 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]]]]] ( 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 , - p z r ) ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) ( - p 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]]]]] ( Γ ( 1 r , ( - 2 b k + b m - p ) z r ) ( ( - 2 b k + b m - p ) z r ) - 1 / r + ( ( 2 b k - b m - p ) z r ) - 1 / r Γ ( 1 r , ( 2 b k - b m - p ) 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]]]]] ( Γ ( 1 r , ( - p - 2 c s + c v ) z r ) ( ( - p - 2 c s + c v ) z r ) - 1 / r + ( ( - p - c ( v - 2 s ) ) z r ) - 1 / r Γ ( 1 r , ( - p - c ( v - 2 s ) ) 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]]]]] ( Γ ( 1 r , ( - 2 b k + b m - p - 2 c s + c v ) z r ) ( ( - 2 b k + b m - p - 2 c s + c v ) z r ) - 1 / r + ( ( 2 b k - b m - p - 2 c s + c v ) z r ) - 1 / r Γ ( 1 r , ( 2 b k - b m - p - 2 c s + c v ) z r ) + ( ( - 2 b k + b m - p + 2 c s - c v ) z r ) - 1 / r Γ ( 1 r , ( - 2 b k + b m - p + 2 c s - c v ) z r ) + ( ( 2 b k - b m - p + 2 c s - c v ) z r ) - 1 / r Γ ( 1 r , ( 2 b k - b m - p + 2 c s - c v ) z r ) ) ) /; m + v + Condition z p z r b z r m c z r v -1 2 -1 m -1 v z r -1 Binomial m m 2 -1 Binomial v v 2 -1 Gamma 1 r -1 -1 p z r 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 -1 p z r -1 r -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 k 0 m -1 2 -1 Binomial m k Gamma 1 r -1 -2 b k b m -1 p z r -2 b k b m -1 p z r -1 r -1 2 b k -1 b m -1 p z r -1 r -1 Gamma 1 r -1 2 b k -1 b m -1 p z r Binomial m m 2 -1 1 -1 \$CellContext`m 2 s 0 v -1 2 -1 Binomial v s Gamma 1 r -1 -1 p -1 2 c s c v z r -1 p -1 2 c s c v z r -1 r -1 -1 p -1 c v -1 2 s z r -1 r -1 Gamma 1 r -1 -1 p -1 c v -1 2 s z r k 0 m -1 2 -1 Binomial m k s 0 v -1 2 -1 Binomial v s Gamma 1 r -1 -2 b k b m -1 p -1 2 c s c v z r -2 b k b m -1 p -1 2 c s c v z r -1 r -1 2 b k -1 b m -1 p -1 2 c s c v z r -1 r -1 Gamma 1 r -1 2 b k -1 b m -1 p -1 2 c s c v z r -2 b k b m -1 p 2 c s -1 c v z r -1 r -1 Gamma 1 r -1 -2 b k b m -1 p 2 c s -1 c v z r 2 b k -1 b m -1 p 2 c s -1 c v z r -1 r -1 Gamma 1 r -1 2 b k -1 b m -1 p 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