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; }

 Tanh

 http://functions.wolfram.com/01.21.21.0169.01

 Input Form

 Integrate[Cos[a z]^m Cosh[b z]^u Tanh[c z], z] == (1/c) (2^(-m - u) Binomial[m, m/2] Binomial[u, u/2] Log[Cosh[c z]] (1 - Mod[m, 2]) (1 - Mod[u, 2])) - 2^(-m - u) Binomial[u, u/2] (-1 + Mod[u, 2]) Sum[Binomial[m, k] (-((1/(a (-2 k + m))) ((I Hypergeometric2F1[-((I a (-2 k + m))/(2 c)), 1, 1 - (I a (-2 k + m))/(2 c), -E^(2 c z)])/ E^(I a (-2 k + m) z))) + (1/(a (-2 k + m))) (I E^(I a (-2 k + m) z) Hypergeometric2F1[(I a (-2 k + m))/(2 c), 1, 1 + (I a (-2 k + m))/(2 c), -E^(2 c z)]) + (E^((2 c - I a (-2 k + m)) z) Hypergeometric2F1[ 1 - (I a (-2 k + m))/(2 c), 1, 2 - (I a (-2 k + m))/(2 c), -E^(2 c z)])/(2 c - I a (-2 k + m)) + (E^((2 c + I a (-2 k + m)) z) Hypergeometric2F1[ 1 + (I a (-2 k + m))/(2 c), 1, 2 + (I a (-2 k + m))/(2 c), -E^(2 c z)])/(2 c + I a (-2 k + m))), {k, 0, Floor[(1/2) (-1 + m)]}] + 2^(-m - u) Binomial[m, m/2] (1 - Mod[m, 2]) Sum[Binomial[u, k] ((1/(b (-2 k + u))) (Hypergeometric2F1[-((b (-2 k + u))/(2 c)), 1, 1 - (b (-2 k + u))/(2 c), -E^(2 c z)]/E^(b (-2 k + u) z)) - (1/(b (-2 k + u))) (E^(b (-2 k + u) z) Hypergeometric2F1[ (b (-2 k + u))/(2 c), 1, 1 + (b (-2 k + u))/(2 c), -E^(2 c z)]) + (E^((2 c - b (-2 k + u)) z) Hypergeometric2F1[ 1 - (b (-2 k + u))/(2 c), 1, 2 - (b (-2 k + u))/(2 c), -E^(2 c z)])/ (2 c - b (-2 k + u)) + (E^((2 c + b (-2 k + u)) z) Hypergeometric2F1[1 + (b (-2 k + u))/(2 c), 1, 2 + (b (-2 k + u))/(2 c), -E^(2 c z)])/(2 c + b (-2 k + u))), {k, 0, Floor[(1/2) (-1 + u)]}] + 2^(-m - u) Sum[Binomial[m, k] Binomial[u, s] (-((E^(((-I) a (-2 k + m) - b (-2 s + u)) z) Hypergeometric2F1[ ((-I) a (-2 k + m) - b (-2 s + u))/(2 c), 1, 1 + ((-I) a (-2 k + m) - b (-2 s + u))/(2 c), -E^(2 c z)])/ ((-I) a (-2 k + m) - b (-2 s + u))) - (E^((I a (-2 k + m) - b (-2 s + u)) z) Hypergeometric2F1[ (I a (-2 k + m) - b (-2 s + u))/(2 c), 1, 1 + (I a (-2 k + m) - b (-2 s + u))/(2 c), -E^(2 c z)])/ (I a (-2 k + m) - b (-2 s + u)) - (E^(((-I) a (-2 k + m) + b (-2 s + u)) z) Hypergeometric2F1[ ((-I) a (-2 k + m) + b (-2 s + u))/(2 c), 1, 1 + ((-I) a (-2 k + m) + b (-2 s + u))/(2 c), -E^(2 c z)])/ ((-I) a (-2 k + m) + b (-2 s + u)) - (E^((I a (-2 k + m) + b (-2 s + u)) z) Hypergeometric2F1[ (I a (-2 k + m) + b (-2 s + u))/(2 c), 1, 1 + (I a (-2 k + m) + b (-2 s + u))/(2 c), -E^(2 c z)])/ (I a (-2 k + m) + b (-2 s + u)) + (E^((2 c - I a (-2 k + m) - b (-2 s + u)) z) Hypergeometric2F1[ 1 + ((-I) a (-2 k + m) - b (-2 s + u))/(2 c), 1, 2 + ((-I) a (-2 k + m) - b (-2 s + u))/(2 c), -E^(2 c z)])/ (2 c - I a (-2 k + m) - b (-2 s + u)) + (E^((2 c + I a (-2 k + m) - b (-2 s + u)) z) Hypergeometric2F1[ 1 + (I a (-2 k + m) - b (-2 s + u))/(2 c), 1, 2 + (I a (-2 k + m) - b (-2 s + u))/(2 c), -E^(2 c z)])/ (2 c + I a (-2 k + m) - b (-2 s + u)) + (E^((2 c - I a (-2 k + m) + b (-2 s + u)) z) Hypergeometric2F1[ 1 + ((-I) a (-2 k + m) + b (-2 s + u))/(2 c), 1, 2 + ((-I) a (-2 k + m) + b (-2 s + u))/(2 c), -E^(2 c z)])/ (2 c - I a (-2 k + m) + b (-2 s + u)) + (E^((2 c + I a (-2 k + m) + b (-2 s + u)) z) Hypergeometric2F1[ 1 + (I a (-2 k + m) + b (-2 s + u))/(2 c), 1, 2 + (I a (-2 k + m) + b (-2 s + u))/(2 c), -E^(2 c z)])/ (2 c + I a (-2 k + m) + b (-2 s + u))), {s, 0, Floor[(1/2) (-1 + u)]}, {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0 && Element[u, Integers] && u > 0

 Standard Form

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 MathML Form

 cos m ( a z ) cosh u ( b z ) tanh ( c z ) z 2 - m - u log ( cosh ( c z ) ) ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - u mod 2 \$CellContext`u 2 ) c ( 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]]]]] ( u u 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity]], List[TagBox[FractionBox["u", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] - 2 - m - u ( u u 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity]], List[TagBox[FractionBox["u", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( u mod 2 \$CellContext`u 2 - 1 ) k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( a ( m - 2 k ) z 2 F 1 ( a ( m - 2 k ) 2 c , 1 ; a ( m - 2 k ) 2 c + 1 ; 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18

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