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/01.20.21.1361.01

 Input Form

 Integrate[z^n E^(p z) Sin[b z] Cosh[c Sqrt[z]], z] == (-I) 2^(-3 - 2 n) ((-E^(-(c^2/(4 ((-I) b + p))))) ((-I) b + p)^(-2 - 2 n) Sum[(-1)^(-h + j) 4^j (-c)^(-h - j + 2 n) (-c + 2 ((-I) b + p) Sqrt[z])^ (h + j) (-((-c + 2 ((-I) b + p) Sqrt[z])^2/((-I) b + p)))^ ((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] ((-c) (-c + 2 ((-I) b + p) Sqrt[z]) Gamma[(1/2) (1 + h + j), -((-c + 2 ((-I) b + p) Sqrt[z])^2/(4 ((-I) b + p)))] + 2 ((-I) b + p) Sqrt[-((-c + 2 ((-I) b + p) Sqrt[z])^2/((-I) b + p))] Gamma[(1/2) (2 + h + j), -((-c + 2 ((-I) b + p) Sqrt[z])^2/ (4 ((-I) b + p)))]), {j, 0, n}, {h, 0, j}] - (((-I) b + p)^(-2 - 2 n) Sum[(-1)^(-h + j) 4^j c^(-h - j + 2 n) (c + 2 ((-I) b + p) Sqrt[z])^(h + j) (-((c + 2 ((-I) b + p) Sqrt[z])^2/((-I) b + p)))^((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] (c (c + 2 ((-I) b + p) Sqrt[z]) Gamma[(1/2) (1 + h + j), -((c + 2 ((-I) b + p) Sqrt[z])^2/ (4 ((-I) b + p)))] + 2 ((-I) b + p) Sqrt[-((c + 2 ((-I) b + p) Sqrt[z])^2/((-I) b + p))] Gamma[(1/2) (2 + h + j), -((c + 2 ((-I) b + p) Sqrt[z])^2/ (4 ((-I) b + p)))]), {j, 0, n}, {h, 0, j}])/ E^(c^2/(4 ((-I) b + p))) + ((I b + p)^(-2 - 2 n) Sum[(-1)^(-h + j) 4^j (-c)^(-h - j + 2 n) (-c + 2 (I b + p) Sqrt[z])^ (h + j) (-((-c + 2 (I b + p) Sqrt[z])^2/(I b + p)))^ ((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] ((-c) (-c + 2 (I b + p) Sqrt[z]) Gamma[(1/2) (1 + h + j), -((-c + 2 (I b + p) Sqrt[z])^2/(4 (I b + p)))] + 2 (I b + p) Sqrt[-((-c + 2 (I b + p) Sqrt[z])^2/(I b + p))] Gamma[(1/2) (2 + h + j), -((-c + 2 (I b + p) Sqrt[z])^2/ (4 (I b + p)))]), {j, 0, n}, {h, 0, j}])/E^(c^2/(4 (I b + p))) + ((I b + p)^(-2 - 2 n) Sum[(-1)^(-h + j) 4^j c^(-h - j + 2 n) (c + 2 (I b + p) Sqrt[z])^(h + j) (-((c + 2 (I b + p) Sqrt[z])^2/(I b + p)))^((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] (c (c + 2 (I b + p) Sqrt[z]) Gamma[(1/2) (1 + h + j), -((c + 2 (I b + p) Sqrt[z])^2/ (4 (I b + p)))] + 2 (I b + p) Sqrt[-((c + 2 (I b + p) Sqrt[z])^2/ (I b + p))] Gamma[(1/2) (2 + h + j), -((c + 2 (I b + p) Sqrt[z])^2/(4 (I b + p)))]), {j, 0, n}, {h, 0, j}])/E^(c^2/(4 (I b + p)))) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n p z sin ( b z ) cosh ( c z ) z - 2 - 2 n - 3 ( - - c 2 4 ( - b + p ) ( j = 0 n h = 0 j ( - 1 ) j - h 4 j ( - c ) - h - j + 2 n ( 2 ( - b + p ) z - c ) h + j ( - ( 2 ( - b + p ) z - c ) 2 - b + p ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 2 ( - b + p ) - ( 2 ( - b + p ) z - c ) 2 - b + p Γ ( 1 2 ( h + j + 2 ) , - ( 2 ( - b + p ) z - c ) 2 4 ( - b + p ) ) - c ( 2 ( - b + p ) z - c ) Γ ( 1 2 ( h + j + 1 ) , - ( 2 ( - b + p ) z - c ) 2 4 ( - b + p ) ) ) ) ( - b + p ) - 2 n - 2 - - c 2 4 ( - b + p ) ( j = 0 n h = 0 j ( - 1 ) j - h 4 j c - h - j + 2 n ( c + 2 ( - b + p ) z ) h + j ( - ( c + 2 ( - b + p ) z ) 2 - b + p ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( c ( c + 2 ( - b + p ) z ) Γ ( 1 2 ( h + j + 1 ) , - ( c + 2 ( - b + p ) z ) 2 4 ( - b + p ) ) + 2 - ( c + 2 ( - b + p ) z ) 2 - b + p ( - b + p ) Γ ( 1 2 ( h + j + 2 ) , - ( c + 2 ( - b + p ) z ) 2 4 ( - b + p ) ) ) ) ( - b + p ) - 2 n - 2 + - c 2 4 ( b + p ) ( b + p ) - 2 n - 2 j = 0 n h = 0 j ( - 1 ) j - h 4 j ( - c ) - h - j + 2 n ( 2 ( b + p ) z - c ) h + j ( - ( 2 ( b + p ) z - c ) 2 b + p ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 2 ( b + p ) - ( 2 ( b + p ) z - c ) 2 b + p Γ ( 1 2 ( h + j + 2 ) , - ( 2 ( b + p ) z - c ) 2 4 ( b + p ) ) - c ( 2 ( b + p ) z - c ) Γ ( 1 2 ( h + j + 1 ) , - ( 2 ( b + p ) z - c ) 2 4 ( b + p ) ) ) + - c 2 4 ( b + p ) ( b + p ) - 2 n - 2 j = 0 n h = 0 j ( - 1 ) j - h 4 j c - h - j + 2 n ( c + 2 ( b + p ) z ) h + j ( - ( c + 2 ( b + p ) z ) 2 b + p ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( c ( c + 2 ( b + p ) z ) Γ ( 1 2 ( h + j + 1 ) , - ( c + 2 ( b + p ) z ) 2 4 ( b + p ) ) + 2 - ( c + 2 ( b + p ) z ) 2 b + p ( b + p ) Γ ( 1 2 ( h + j + 2 ) , - ( c + 2 ( b + p ) z ) 2 4 ( b + p ) ) ) ) /; n Condition z z n p z b z c z 1 2 -1 2 -2 n -3 -1 -1 c 2 4 -1 b p -1 h 0 j j 0 n -1 j -1 h 4 j -1 c -1 h -1 j 2 n 2 -1 b p z 1 2 -1 c h j -1 2 -1 b p z 1 2 -1 c 2 -1 b p -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j 2 -1 b p -1 2 -1 b p z 1 2 -1 c 2 -1 b p -1 1 2 Gamma 1 2 h j 2 -1 2 -1 b p z 1 2 -1 c 2 4 -1 b p -1 -1 c 2 -1 b p z 1 2 -1 c Gamma 1 2 h j 1 -1 2 -1 b p z 1 2 -1 c 2 4 -1 b p -1 -1 b p -2 n -2 -1 -1 c 2 4 -1 b p -1 h 0 j j 0 n -1 j -1 h 4 j c -1 h -1 j 2 n c 2 -1 b p z 1 2 h j -1 c 2 -1 b p z 1 2 2 -1 b p -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j c c 2 -1 b p z 1 2 Gamma 1 2 h j 1 -1 c 2 -1 b p z 1 2 2 4 -1 b p -1 2 -1 c 2 -1 b p z 1 2 2 -1 b p -1 1 2 -1 b p Gamma 1 2 h j 2 -1 c 2 -1 b p z 1 2 2 4 -1 b p -1 -1 b p -2 n -2 -1 c 2 4 b p -1 b p -2 n -2 h 0 j j 0 n -1 j -1 h 4 j -1 c -1 h -1 j 2 n 2 b p z 1 2 -1 c h j -1 2 b p z 1 2 -1 c 2 b p -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j 2 b p -1 2 b p z 1 2 -1 c 2 b p -1 1 2 Gamma 1 2 h j 2 -1 2 b p z 1 2 -1 c 2 4 b p -1 -1 c 2 b p z 1 2 -1 c Gamma 1 2 h j 1 -1 2 b p z 1 2 -1 c 2 4 b p -1 -1 c 2 4 b p -1 b p -2 n -2 h 0 j j 0 n -1 j -1 h 4 j c -1 h -1 j 2 n c 2 b p z 1 2 h j -1 c 2 b p z 1 2 2 b p -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j c c 2 b p z 1 2 Gamma 1 2 h j 1 -1 c 2 b p z 1 2 2 4 b p -1 2 -1 c 2 b p z 1 2 2 b p -1 1 2 b p Gamma 1 2 h j 2 -1 c 2 b p z 1 2 2 4 b p -1 n [/itex]

 Rule Form

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

 2002-12-18