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/01.20.21.1448.01

 Input Form

 Integrate[z^n E^(p Sqrt[z]) Cos[b Sqrt[z]]^m Cosh[c Sqrt[z]], z] == (-2^(-m)) Binomial[m, m/2] (Gamma[2 (1 + n), (-c - p) Sqrt[z]]/ (-c - p)^(2 (1 + n)) + Gamma[2 (1 + n), (c - p) Sqrt[z]]/ (c - p)^(2 (1 + n))) (1 - Mod[m, 2]) - Sum[Binomial[m, s] (Gamma[2 (1 + n), (-c - p - I b (m - 2 s)) Sqrt[z]]/ (-c - p - I b (m - 2 s))^(2 (1 + n)) + Gamma[2 (1 + n), (c - p - I b (m - 2 s)) Sqrt[z]]/ (c - p - I b (m - 2 s))^(2 (1 + n)) + Gamma[2 (1 + n), (-c - p + I b (m - 2 s)) Sqrt[z]]/ (-c - p + I b (m - 2 s))^(2 (1 + n)) + Gamma[2 (1 + n), (c - p + I b (m - 2 s)) Sqrt[z]]/ (c - p + I b (m - 2 s))^(2 (1 + n))), {s, 0, Floor[(1/2) (-1 + m)]}]/ 2^m /; Element[m, Integers] && m > 0 && Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n p z cos m ( b z ) cosh ( c z ) z - 2 - m ( 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]]]]] ( Γ ( 2 ( n + 1 ) , ( - c - p ) z ) ( - c - p ) - 2 ( n + 1 ) + ( c - p ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( c - p ) z ) ) ( 1 - m mod 2 \$CellContext`m 2 ) - 2 - m s = 0 m - 1 2 ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( Γ ( 2 ( n + 1 ) , ( - c - p + b ( m - 2 s ) ) z ) ( - c - p + b ( m - 2 s ) ) - 2 ( n + 1 ) + ( c - p + b ( m - 2 s ) ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( c - p + b ( m - 2 s ) ) z ) + ( - c - p - b ( m - 2 s ) ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - c - p - b ( m - 2 s ) ) z ) + ( c - p - b ( m - 2 s ) ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( c - p - b ( m - 2 s ) ) z ) ) /; m + n Condition z z n p z 1 2 b z 1 2 m c z 1 2 -1 2 -1 m Binomial m m 2 -1 Gamma 2 n 1 -1 c -1 p z 1 2 -1 c -1 p -2 n 1 c -1 p -2 n 1 Gamma 2 n 1 c -1 p z 1 2 1 -1 \$CellContext`m 2 -1 2 -1 m s 0 m -1 2 -1 Binomial m s Gamma 2 n 1 -1 c -1 p b m -1 2 s z 1 2 -1 c -1 p b m -1 2 s -2 n 1 c -1 p b m -1 2 s -2 n 1 Gamma 2 n 1 c -1 p b m -1 2 s z 1 2 -1 c -1 p -1 b m -1 2 s -2 n 1 Gamma 2 n 1 -1 c -1 p -1 b m -1 2 s z 1 2 c -1 p -1 b m -1 2 s -2 n 1 Gamma 2 n 1 c -1 p -1 b m -1 2 s z 1 2 m SuperPlus n [/itex]

 Rule Form

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

 2002-12-18