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/01.20.21.4509.01

 Input Form

 Integrate[z^n Sinh[d z + e] Cosh[c z^2 + f z + g]^v, z] == 2^(-2 - v) ((2 d^(-1 - n) Binomial[v, v/2] (E^(2 e) (-1)^n Gamma[1 + n, (-d) z] + Gamma[1 + n, d z]) (1 - Mod[v, 2]))/E^e + Sum[E^(-e + 2 g s - g v) Binomial[v, s] (c (-2 s + v))^(-n - 1) (E^(2 g (-2 s + v) + (-d - 2 f s + f v)^2/(c (8 s - 4 v))) Sum[2^(-n + q) (d + 2 f s - f v)^(n - q) (-d - (2 s - v) (f + 2 c z))^ (1 + q) ((d + (2 s - v) (f + 2 c z))^2/(c (2 s - v)))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (-d - 2 f s + f v - 4 c s z + 2 c v z)^2/(8 c s - 4 c v)], {q, 0, n}] - E^(2 e + 2 g (-2 s + v) + (d + f (-2 s + v))^2/ (c (8 s - 4 v))) Sum[(-(d/2) + f (s - v/2))^(n - q) ((d - 2 f s + f v - 4 c s z + 2 c v z)^2/(2 c s - c v))^ ((1/2) (-1 - q)) (d - (2 s - v) (f + 2 c z))^(1 + q) Binomial[n, q] Gamma[(1 + q)/2, (d - 2 f s + f v - 4 c s z + 2 c v z)^2/(8 c s - 4 c v)], {q, 0, n}] - E^(2 e - (-d - 2 f s + f v)^2/(c (8 s - 4 v))) (-1)^n Sum[2^(-n + q) (-d - 2 f s + f v)^(n - q) (-d - (2 s - v) (f + 2 c z)) (d + (2 s - v) (f + 2 c z))^q (-((d + (2 s - v) (f + 2 c z))^2/(c (2 s - v))))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((-d - (2 s - v) (f + 2 c z))^2/ (c (8 s - 4 v)))], {q, 0, n}] - ((-1)^n Sum[2^(-n + q) (d + f (-2 s + v))^(n - q) (-d + (2 s - v) (f + 2 c z))^(1 + q) (-((-d + (2 s - v) (f + 2 c z))^2/(c (2 s - v))))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((-d + (2 s - v) (f + 2 c z))^2/ (c (8 s - 4 v)))], {q, 0, n}])/E^((d + f (-2 s + v))^2/ (c (8 s - 4 v)))), {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 + f z + g ) z 2 - v - 2 ( 2 - 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 ) d - n - 1 + s = 0 v - 1 2 - e + 2 g s - g v ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( c ( v - 2 s ) ) - n - 1 ( - - ( d + f ( v - 2 s ) ) 2 c ( 8 s - 4 v ) ( - 1 ) n q = 0 n 2 q - n ( d + f ( v - 2 s ) ) n - q ( ( 2 s - v ) ( f + 2 c z ) - d ) q + 1 ( - ( ( 2 s - v ) ( f + 2 c z ) - d ) 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 , - ( ( 2 s - v ) ( f + 2 c z ) - d ) 2 c ( 8 s - 4 v ) ) - 2 e - ( - d - 2 f s + f v ) 2 c ( 8 s - 4 v ) ( - 1 ) n q = 0 n 2 q - n ( - d - 2 f s + f v ) n - q ( - d - ( 2 s - v ) ( f + 2 c z ) ) ( d + ( 2 s - v ) ( f + 2 c z ) ) q ( - ( d + ( 2 s - v ) ( f + 2 c 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 - ( 2 s - v ) ( f + 2 c z ) ) 2 c ( 8 s - 4 v ) ) + ( - d - 2 f s + f v ) 2 c ( 8 s - 4 v ) + 2 g ( v - 2 s ) q = 0 n 2 q - n ( d + 2 f s - f v ) n - q ( - d - ( 2 s - v ) ( f + 2 c z ) ) q + 1 ( ( d + ( 2 s - v ) ( f + 2 c 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 - 2 f s + f v - 4 c s z + 2 c v z ) 2 8 c s - 4 c v ) - ( d + f ( v - 2 s ) ) 2 c ( 8 s - 4 v ) + 2 e + 2 g ( v - 2 s ) q = 0 n ( f ( s - v 2 ) - d 2 ) n - q ( ( d - 2 f s + f v - 4 c s z + 2 c v z ) 2 2 c s - c v ) 1 2 ( - q - 1 ) ( d - ( 2 s - v ) ( f + 2 c z ) ) 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 - 2 f s + f v - 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 f z g v 2 -1 v -2 2 -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 d -1 n -1 s 0 v -1 2 -1 -1 e 2 g s -1 g v Binomial v s c v -1 2 s -1 n -1 -1 -1 d f v -1 2 s 2 c 8 s -1 4 v -1 -1 n q 0 n 2 q -1 n d f v -1 2 s n -1 q 2 s -1 v f 2 c z -1 d q 1 -1 2 s -1 v f 2 c z -1 d 2 c 2 s -1 v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 2 s -1 v f 2 c z -1 d 2 c 8 s -1 4 v -1 -1 2 e -1 -1 d -1 2 f s f v 2 c 8 s -1 4 v -1 -1 n q 0 n 2 q -1 n -1 d -1 2 f s f v n -1 q -1 d -1 2 s -1 v f 2 c z d 2 s -1 v f 2 c z q -1 d 2 s -1 v f 2 c z 2 c 2 s -1 v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 -1 d -1 2 s -1 v f 2 c z 2 c 8 s -1 4 v -1 -1 d -1 2 f s f v 2 c 8 s -1 4 v -1 2 g v -1 2 s q 0 n 2 q -1 n d 2 f s -1 f v n -1 q -1 d -1 2 s -1 v f 2 c z q 1 d 2 s -1 v f 2 c z 2 c 2 s -1 v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 d -1 2 f s f v -1 4 c s z 2 c v z 2 8 c s -1 4 c v -1 -1 d f v -1 2 s 2 c 8 s -1 4 v -1 2 e 2 g v -1 2 s q 0 n f s -1 v 2 -1 -1 d 2 -1 n -1 q d -1 2 f s f v -1 4 c s z 2 c v z 2 2 c s -1 c v -1 1 2 -1 q -1 d -1 2 s -1 v f 2 c z q 1 Binomial n q Gamma q 1 2 -1 d -1 2 f s f v -1 4 c s z 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