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/01.20.21.0901.01

 Input Form

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

 Standard Form

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 MathML Form

 z n sin ( z b + e + d z ) cosh ( g + f z ) z 2 - 2 n - 3 ( - b 2 4 ( d - f ) - g + e ( j = 0 n h = 0 j ( - 1 ) j - h 4 j ( b ) - h - j + 2 n ( 2 z ( d - f ) + b ) h + j ( - ( 2 z ( d - f ) + b ) 2 d - f ) 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]]]]] ( b ( 2 z ( d - f ) + b ) Γ ( 1 2 ( h + j + 1 ) , - ( 2 z ( d - f ) + b ) 2 4 ( d - f ) ) + 2 - ( 2 z ( d - f ) + b ) 2 d - f ( d - f ) Γ ( 1 2 ( h + j + 2 ) , - ( 2 z ( d - f ) + b ) 2 4 ( d - f ) ) ) ) ( d - f ) - 2 ( n + 1 ) + b 2 4 ( - f + - d ) - g - e ( f + d ) - 2 ( n + 1 ) j = 0 n h = 0 j ( - 1 ) j - h 4 j ( - b ) - h - j + 2 n ( 2 ( - f - d ) z - b ) h + j ( - ( 2 ( - f - d ) z - b ) 2 - f - d ) 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 ( - f - d ) - ( 2 ( - f - d ) z - b ) 2 - f - d Γ ( 1 2 ( h + j + 2 ) , - ( 2 ( - f - d ) z - b ) 2 4 ( - f - d ) ) - b ( 2 ( - f - d ) z - b ) Γ ( 1 2 ( h + j + 1 ) , - ( 2 ( - f - d ) z - b ) 2 4 ( - f - d ) ) ) + b 2 4 ( f - d ) + g - e ( f - d ) - 2 ( n + 1 ) j = 0 n h = 0 j ( - 1 ) j - h 4 j ( - b ) - h - j + 2 n ( 2 ( f - d ) z - b ) h + j ( - ( 2 ( f - d ) z - b ) 2 f - d ) 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 ( f - d ) - ( 2 ( f - d ) z - b ) 2 f - d Γ ( 1 2 ( h + j + 2 ) , - ( 2 ( f - d ) z - b ) 2 4 ( f - d ) ) - b ( 2 ( f - d ) z - b ) Γ ( 1 2 ( h + j + 1 ) , - ( 2 ( f - d ) z - b ) 2 4 ( f - d ) ) ) - b 2 4 ( f + d ) + g + e ( f + d ) - 2 ( n + 1 ) j = 0 n h = 0 j ( - 1 ) j - h 4 j ( b ) - h - j + 2 n ( 2 z ( f + d ) + b ) h + j ( - ( 2 z ( f + d ) + b ) 2 f + d ) 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]]]]] ( b ( 2 z ( f + d ) + b ) Γ ( 1 2 ( h + j + 1 ) , - ( 2 z ( f + d ) + b ) 2 4 ( f + d ) ) + 2 - ( 2 z ( f + d ) + b ) 2 f + d ( f + d ) Γ ( 1 2 ( h + j + 2 ) , - ( 2 z ( f + d ) + b ) 2 4 ( f + d ) ) ) ) /; n Condition z z n z 1 2 b e d z g f z 2 -2 n -3 -1 b 2 4 d -1 f -1 -1 g e h 0 j j 0 n -1 j -1 h 4 j b -1 h -1 j 2 n 2 z 1 2 d -1 f b h j -1 2 z 1 2 d -1 f b 2 d -1 f -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j b 2 z 1 2 d -1 f b Gamma 1 2 h j 1 -1 2 z 1 2 d -1 f b 2 4 d -1 f -1 2 -1 2 z 1 2 d -1 f b 2 d -1 f -1 1 2 d -1 f Gamma 1 2 h j 2 -1 2 z 1 2 d -1 f b 2 4 d -1 f -1 d -1 f -2 n 1 b 2 4 -1 f -1 d -1 -1 g -1 e f d -2 n 1 h 0 j j 0 n -1 j -1 h 4 j -1 b -1 h -1 j 2 n 2 -1 f -1 d z 1 2 -1 b h j -1 2 -1 f -1 d z 1 2 -1 b 2 -1 f -1 d -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j 2 -1 f -1 d -1 2 -1 f -1 d z 1 2 -1 b 2 -1 f -1 d -1 1 2 Gamma 1 2 h j 2 -1 2 -1 f -1 d z 1 2 -1 b 2 4 -1 f -1 d -1 -1 b 2 -1 f -1 d z 1 2 -1 b Gamma 1 2 h j 1 -1 2 -1 f -1 d z 1 2 -1 b 2 4 -1 f -1 d -1 b 2 4 f -1 d -1 g -1 e f -1 d -2 n 1 h 0 j j 0 n -1 j -1 h 4 j -1 b -1 h -1 j 2 n 2 f -1 d z 1 2 -1 b h j -1 2 f -1 d z 1 2 -1 b 2 f -1 d -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j 2 f -1 d -1 2 f -1 d z 1 2 -1 b 2 f -1 d -1 1 2 Gamma 1 2 h j 2 -1 2 f -1 d z 1 2 -1 b 2 4 f -1 d -1 -1 b 2 f -1 d z 1 2 -1 b Gamma 1 2 h j 1 -1 2 f -1 d z 1 2 -1 b 2 4 f -1 d -1 -1 b 2 4 f d -1 g e f d -2 n 1 h 0 j j 0 n -1 j -1 h 4 j b -1 h -1 j 2 n 2 z 1 2 f d b h j -1 2 z 1 2 f d b 2 f d -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j b 2 z 1 2 f d b Gamma 1 2 h j 1 -1 2 z 1 2 f d b 2 4 f d -1 2 -1 2 z 1 2 f d b 2 f d -1 1 2 f d Gamma 1 2 h j 2 -1 2 z 1 2 f d b 2 4 f d -1 n [/itex]

 Rule Form

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

 2002-12-18