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/01.20.21.1047.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18