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/01.20.21.0516.01

 Input Form

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

 Standard Form

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 MathML Form

 z n e + d z cosh ( z c + g + f z ) z 2 - 2 n - 2 ( - c 2 4 ( d - f ) + e - g ( k = 0 n h = 0 k ( - 1 ) k - h 4 k ( - c ) - h - k + 2 n ( 2 ( d - f ) z - c ) h + k ( - ( 2 ( d - f ) z - c ) 2 d - f ) 1 2 ( - h - k - 1 ) ( k h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 2 ( d - f ) - ( 2 ( d - f ) z - c ) 2 d - f Γ ( 1 2 ( h + k + 2 ) , - ( 2 ( d - f ) z - c ) 2 4 ( d - f ) ) - c ( 2 ( d - f ) z - c ) Γ ( 1 2 ( h + k + 1 ) , - ( 2 ( d - f ) z - c ) 2 4 ( d - f ) ) ) ) ( d - f ) - 2 n - 2 + - c 2 4 ( d + f ) + e + g ( d + f ) - 2 n - 2 k = 0 n h = 0 k ( - 1 ) k - h 4 k c - h - k + 2 n ( c + 2 ( d + f ) z ) h + k ( - ( c + 2 ( d + f ) z ) 2 d + f ) 1 2 ( - h - k - 1 ) ( k h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( c ( c + 2 ( d + f ) z ) Γ ( 1 2 ( h + k + 1 ) , - ( c + 2 ( d + f ) z ) 2 4 ( d + f ) ) + 2 - ( c + 2 ( d + f ) z ) 2 d + f ( d + f ) Γ ( 1 2 ( h + k + 2 ) , - ( c + 2 ( d + f ) z ) 2 4 ( d + f ) ) ) ) /; n Condition z z n e d z z 1 2 c g f z 2 -2 n -2 -1 c 2 4 d -1 f -1 e -1 g h 0 k k 0 n -1 k -1 h 4 k -1 c -1 h -1 k 2 n 2 d -1 f z 1 2 -1 c h k -1 2 d -1 f z 1 2 -1 c 2 d -1 f -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k 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 k 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 k 1 -1 2 d -1 f z 1 2 -1 c 2 4 d -1 f -1 d -1 f -2 n -2 -1 c 2 4 d f -1 e g d f -2 n -2 h 0 k k 0 n -1 k -1 h 4 k c -1 h -1 k 2 n c 2 d f z 1 2 h k -1 c 2 d f z 1 2 2 d f -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k c c 2 d f z 1 2 Gamma 1 2 h k 1 -1 c 2 d f z 1 2 2 4 d f -1 2 -1 c 2 d f z 1 2 2 d f -1 1 2 d f Gamma 1 2 h k 2 -1 c 2 d f z 1 2 2 4 d f -1 n [/itex]

 Rule Form

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

 2002-12-18