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/01.20.21.4483.01

 Input Form

 Integrate[z^n Sinh[d z + e] Cosh[c z^2 + g]^v, z] == 2^(-2 - v) ((2 d^(-1 - n) Binomial[v, v/2] ((-1)^n E^(2 e) Gamma[1 + n, (-d) z] + Gamma[1 + n, d z]) (1 - Mod[v, 2]))/E^e - c^(-1 - n) Sum[E^((-d^2 + 4 c (2 s - v) (e + 2 g s - g v))/(c (8 s - 4 v))) (-2 s + v)^(-1 - n) Binomial[v, s] ((-E^(-2 e + d^2/(c (4 s - 2 v)) + 2 g (-2 s + v))) Sum[2^(-n + q) d^(n - q) ((d + 4 c s z - 2 c v z)^2/(2 c s - c v))^ ((1/2) (-1 - q)) (-d + 2 c (-2 s + v) z)^(1 + q) Binomial[n, q] Gamma[(1 + q)/2, (d + 4 c s z - 2 c v z)^2/(c (8 s - 4 v))], {q, 0, n}] - (-1)^n Sum[2^(-n + q) (-d)^(n - q) (d + 4 c s z - 2 c v z)^(1 + q) (-((d + 4 c s z - 2 c v z)^2/ (2 c s - c v)))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((d + 4 c s z - 2 c v z)^2/(8 c s - 4 c v))], {q, 0, n}] + ((-1)^n Sum[2^(-n + q) d^(n - q) (-d + 4 c s z - 2 c v z)^(1 + q) (-((d + 2 c (-2 s + v) z)^2/(c (2 s - v))))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((d - 4 c s z + 2 c v z)^2/(8 c s - 4 c v))], {q, 0, n}])/E^(2 e) - E^(2 g (-2 s + v) + d^2/(4 c s - 2 c v)) Sum[2^(-n + q) (-d)^(n - q) (-d + 4 c s z - 2 c v z) (d + 2 c (-2 s + v) z)^q ((d + 2 c (-2 s + v) z)^2/(c (2 s - v)))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (d - 4 c s z + 2 c v z)^2/(8 c s - 4 c v)], {q, 0, n}]), {s, 0, Floor[(1/2) (-1 + v)]}]) /; Element[n, Integers] && n >= 0 && Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

 z n sinh ( e + d z ) cosh v ( c z 2 + g ) z 2 - v - 2 ( 2 d - n - 1 - e ( 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 ) n 2 e Γ ( n + 1 , - d z ) + Γ ( n + 1 , d z ) ) ( 1 - v mod 2 \$CellContext`v 2 ) - c - n - 1 s = 0 v - 1 2 4 c ( 2 s - v ) ( e + 2 g s - g v ) - d 2 c ( 8 s - 4 v ) ( v - 2 s ) - n - 1 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - d 2 c ( 4 s - 2 v ) - 2 e + 2 g ( v - 2 s ) q = 0 n 2 q - n d n - q ( ( d + 4 c s z - 2 c v z ) 2 2 c s - c v ) 1 2 ( - q - 1 ) ( 2 c ( v - 2 s ) z - d ) q + 1 ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( d + 4 c s z - 2 c v z ) 2 c ( 8 s - 4 v ) ) - d 2 4 c s - 2 c v + 2 g ( v - 2 s ) q = 0 n 2 q - n ( - d ) n - q ( - d + 4 c s z - 2 c v z ) ( d + 2 c ( v - 2 s ) z ) q ( ( d + 2 c ( v - 2 s ) z ) 2 c ( 2 s - v ) ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( d - 4 c s z + 2 c v z ) 2 8 c s - 4 c v ) + ( - 1 ) n - 2 e q = 0 n 2 q - n d n - q ( - d + 4 c s z - 2 c v z ) q + 1 ( - ( d + 2 c ( v - 2 s ) z ) 2 c ( 2 s - v ) ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( d - 4 c s z + 2 c v z ) 2 8 c s - 4 c v ) - ( - 1 ) n q = 0 n 2 q - n ( - d ) n - q ( d + 4 c s z - 2 c v z ) q + 1 ( - ( d + 4 c s z - 2 c v z ) 2 2 c s - c v ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( d + 4 c s z - 2 c v z ) 2 8 c s - 4 c v ) ) ) /; n v + Condition z z n e d z c z 2 g v 2 -1 v -2 2 d -1 n -1 -1 e Binomial v v 2 -1 -1 n 2 e Gamma n 1 -1 d z Gamma n 1 d z 1 -1 \$CellContext`v 2 -1 c -1 n -1 s 0 v -1 2 -1 4 c 2 s -1 v e 2 g s -1 g v -1 d 2 c 8 s -1 4 v -1 v -1 2 s -1 n -1 Binomial v s -1 d 2 c 4 s -1 2 v -1 -1 2 e 2 g v -1 2 s q 0 n 2 q -1 n d n -1 q d 4 c s z -1 2 c v z 2 2 c s -1 c v -1 1 2 -1 q -1 2 c v -1 2 s z -1 d q 1 Binomial n q Gamma q 1 2 -1 d 4 c s z -1 2 c v z 2 c 8 s -1 4 v -1 -1 d 2 4 c s -1 2 c v -1 2 g v -1 2 s q 0 n 2 q -1 n -1 d n -1 q -1 d 4 c s z -1 2 c v z d 2 c v -1 2 s z q d 2 c v -1 2 s z 2 c 2 s -1 v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 d -1 4 c s z 2 c v z 2 8 c s -1 4 c v -1 -1 n -2 e q 0 n 2 q -1 n d n -1 q -1 d 4 c s z -1 2 c v z q 1 -1 d 2 c v -1 2 s z 2 c 2 s -1 v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 d -1 4 c s z 2 c v z 2 8 c s -1 4 c v -1 -1 -1 n q 0 n 2 q -1 n -1 d n -1 q d 4 c s z -1 2 c v z q 1 -1 d 4 c s z -1 2 c v z 2 2 c s -1 c v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 d 4 c s z -1 2 c v z 2 8 c s -1 4 c v -1 n v SuperPlus [/itex]

 Rule Form

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

 2002-12-18