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/01.20.21.0385.01

 Input Form

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

 Standard Form

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 MathML Form

 z n z b + e + d z cosh ( c z ) z 2 - 2 n - 2 d - 2 n - 2 ( e - ( b - c ) 2 4 d k = 0 n h = 0 k ( - 1 ) k - h 4 k ( b - c ) - h - k + 2 n ( b - c + 2 d z ) h + k ( - ( b - c + 2 d z ) 2 d ) 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]]]]] ( ( b - c ) ( b - c + 2 d z ) Γ ( 1 2 ( h + k + 1 ) , - ( b - c + 2 d z ) 2 4 d ) + 2 - ( b - c + 2 d z ) 2 d d Γ ( 1 2 ( h + k + 2 ) , - ( b - c + 2 d z ) 2 4 d ) ) + e - ( b + c ) 2 4 d k = 0 n h = 0 k ( - 1 ) k - h 4 k ( b + c ) - h - k + 2 n ( b + c + 2 d z ) h + k ( - ( b + c + 2 d z ) 2 d ) 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]]]]] ( ( b + c ) ( b + c + 2 d z ) Γ ( 1 2 ( h + k + 1 ) , - ( b + c + 2 d z ) 2 4 d ) + 2 - ( b + c + 2 d z ) 2 d d Γ ( 1 2 ( h + k + 2 ) , - ( b + c + 2 d z ) 2 4 d ) ) ) /; n Condition z z n z 1 2 b e d z c z 1 2 2 -2 n -2 d -2 n -2 e -1 b -1 c 2 4 d -1 h 0 k k 0 n -1 k -1 h 4 k b -1 c -1 h -1 k 2 n b -1 c 2 d z 1 2 h k -1 b -1 c 2 d z 1 2 2 d -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k b -1 c b -1 c 2 d z 1 2 Gamma 1 2 h k 1 -1 b -1 c 2 d z 1 2 2 4 d -1 2 -1 b -1 c 2 d z 1 2 2 d -1 1 2 d Gamma 1 2 h k 2 -1 b -1 c 2 d z 1 2 2 4 d -1 e -1 b c 2 4 d -1 h 0 k k 0 n -1 k -1 h 4 k b c -1 h -1 k 2 n b c 2 d z 1 2 h k -1 b c 2 d z 1 2 2 d -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k b c b c 2 d z 1 2 Gamma 1 2 h k 1 -1 b c 2 d z 1 2 2 4 d -1 2 -1 b c 2 d z 1 2 2 d -1 1 2 d Gamma 1 2 h k 2 -1 b c 2 d z 1 2 2 4 d -1 n [/itex]

 Rule Form

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

 2002-12-18