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/01.20.21.1306.01

 Input Form

 Integrate[E^(b Sqrt[z] + e) Cos[a Sqrt[z] + q]^m Cosh[c Sqrt[z] + g], z] == (((E^(e - g + (b - c) Sqrt[z]) (-1 + b Sqrt[z] - c Sqrt[z]))/(-b + c)^2 + (E^(e + g + (b + c) Sqrt[z]) (-1 + b Sqrt[z] + c Sqrt[z]))/(b + c)^2) Binomial[m, m/2] (1 - Mod[m, 2]))/2^m + Sum[((E^(e - g + I (-2 k + m) q + (b - c + I a (-2 k + m)) Sqrt[z]) (-1 + b Sqrt[z] - (c - I a (-2 k + m)) Sqrt[z]))/ (-b + c - I a (-2 k + m))^2 + (E^(e + g - I (-2 k + m) q + (b + c - I a (-2 k + m)) Sqrt[z]) (-1 + b Sqrt[z] + (c - I a (-2 k + m)) Sqrt[z]))/ (b + c - I a (-2 k + m))^2 + (E^(e - g - I (-2 k + m) q + (b - c - I a (-2 k + m)) Sqrt[z]) (-1 + b Sqrt[z] - (c + I a (-2 k + m)) Sqrt[z]))/ (-b + c + I a (-2 k + m))^2 + (E^(e + g + I (-2 k + m) q + (b + c + I a (-2 k + m)) Sqrt[z]) (-1 + b Sqrt[z] + (c + I a (-2 k + m)) Sqrt[z]))/ (b + c + I a (-2 k + m))^2) Binomial[m, k], {k, 0, Floor[(1/2) (-1 + m)]}]/2^m /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 z b + e cos m ( z a + q ) cosh ( z c + g ) z 2 - m ( z ( b + c ) + e + g ( z b + c z - 1 ) ( b + c ) 2 + z ( b - c ) + e - g ( z b - c z - 1 ) ( c - b ) 2 ) ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) + 2 - m k = 0 m - 1 2 ( e + g + ( m - 2 k ) q + ( b + c + a ( m - 2 k ) ) z ( z b + ( c + a ( m - 2 k ) ) z - 1 ) ( b + c + a ( m - 2 k ) ) 2 + e + g - ( m - 2 k ) q + ( b + c - a ( m - 2 k ) ) z ( z b + ( c - a ( m - 2 k ) ) z - 1 ) ( b + c - a ( m - 2 k ) ) 2 + e - g - ( m - 2 k ) q + ( b - c - a ( m - 2 k ) ) z ( z b - ( c + a ( m - 2 k ) ) z - 1 ) ( - b + c + a ( m - 2 k ) ) 2 + e - g + ( m - 2 k ) q + ( b - c + a ( m - 2 k ) ) z ( z b - ( c - a ( m - 2 k ) ) z - 1 ) ( - b + c - a ( m - 2 k ) ) 2 ) ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] /; m + Condition z z 1 2 b e z 1 2 a q m z 1 2 c g 2 -1 m z 1 2 b c e g z 1 2 b c z 1 2 -1 b c 2 -1 z 1 2 b -1 c e -1 g z 1 2 b -1 c z 1 2 -1 c -1 b 2 -1 Binomial m m 2 -1 1 -1 \$CellContext`m 2 2 -1 m k 0 m -1 2 -1 e g m -1 2 k q b c a m -1 2 k z 1 2 z 1 2 b c a m -1 2 k z 1 2 -1 b c a m -1 2 k 2 -1 e g -1 m -1 2 k q b c -1 a m -1 2 k z 1 2 z 1 2 b c -1 a m -1 2 k z 1 2 -1 b c -1 a m -1 2 k 2 -1 e -1 g -1 m -1 2 k q b -1 c -1 a m -1 2 k z 1 2 z 1 2 b -1 c a m -1 2 k z 1 2 -1 -1 b c a m -1 2 k 2 -1 e -1 g m -1 2 k q b -1 c a m -1 2 k z 1 2 z 1 2 b -1 c -1 a m -1 2 k z 1 2 -1 -1 b c -1 a m -1 2 k 2 -1 Binomial m k m SuperPlus [/itex]

 Rule Form

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

 2002-12-18