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/01.20.21.0931.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18