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/01.20.21.1219.01

 Input Form

 Integrate[E^(p z) Sin[b z^2]^m Cosh[c z], z] == (1/((c - p) (c + p))) ((E^(p z) Binomial[m, m/2] (1 - Mod[m, 2]) ((-p) Cosh[c z] + c Sinh[c z]))/2^m) + (1/b) (I 2^(-2 - m) Sqrt[Pi] Sum[(1/(2 k - m)) ((-1)^k Binomial[m, k] ((Sqrt[(-I) b (2 k - m)] Erfi[(-c + p - 2 I b (2 k - m) z)/ (2 Sqrt[(-I) b (2 k - m)])])/ E^((I ((-c + p)^2 + 2 b (2 k - m) m Pi))/(4 b (2 k - m))) - E^((I ((c + p)^2 + 2 b (2 k - m) m Pi))/(4 b (2 k - m))) Sqrt[I b (2 k - m)] Erfi[(c + p + 2 I b (2 k - m) z)/ (2 Sqrt[I b (2 k - m)])] - (Sqrt[(-I) b (-2 k + m)] Erfi[(-c + p - 2 I b (-2 k + m) z)/(2 Sqrt[(-I) b (-2 k + m)])])/ E^((I ((-c + p)^2 - 2 b m (-2 k + m) Pi))/(4 b (-2 k + m))) + E^((I ((c + p)^2 - 2 b m (-2 k + m) Pi))/(4 b (-2 k + m))) Sqrt[I b (-2 k + m)] Erfi[(c + p + 2 I b (-2 k + m) z)/ (2 Sqrt[I b (-2 k + m)])])), {k, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 p z sin m ( b z 2 ) cosh ( c z ) z 2 - m p z ( 1 - m mod 2 \$CellContext`m 2 ) ( c sinh ( c z ) - p cosh ( c z ) ) ( c - p ) ( c + p ) ( 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]]]]] + 2 - m - 2 π b k = 0 m - 1 2 1 2 k - m ( ( - 1 ) k ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( ( p - c ) 2 + 2 b ( 2 k - m ) m π ) 4 b ( 2 k - m ) - b ( 2 k - m ) erfi ( - c + p - 2 b ( 2 k - m ) z 2 - b ( 2 k - m ) ) - ( ( c + p ) 2 + 2 b ( 2 k - m ) m π ) 4 b ( 2 k - m ) b ( 2 k - m ) erfi ( c + p + 2 b ( 2 k - m ) z 2 b ( 2 k - m ) ) - - ( ( p - c ) 2 - 2 b m ( m - 2 k ) π ) 4 b ( m - 2 k ) - b ( m - 2 k ) erfi ( - c + p - 2 b ( m - 2 k ) z 2 - b ( m - 2 k ) ) + ( ( c + p ) 2 - 2 b m ( m - 2 k ) π ) 4 b ( m - 2 k ) b ( m - 2 k ) erfi ( c + p + 2 b ( m - 2 k ) z 2 b ( m - 2 k ) ) ) ) /; m + Condition z p z b z 2 m c z 2 -1 m p z 1 -1 \$CellContext`m 2 c c z -1 p c z c -1 p c p -1 Binomial m m 2 -1 2 -1 m -2 1 2 b -1 k 0 m -1 2 -1 1 2 k -1 m -1 -1 k Binomial m k -1 p -1 c 2 2 b 2 k -1 m m 4 b 2 k -1 m -1 -1 b 2 k -1 m 1 2 Erfi -1 c p -1 2 b 2 k -1 m z 2 -1 b 2 k -1 m 1 2 -1 -1 c p 2 2 b 2 k -1 m m 4 b 2 k -1 m -1 b 2 k -1 m 1 2 Erfi c p 2 b 2 k -1 m z 2 b 2 k -1 m 1 2 -1 -1 -1 p -1 c 2 -1 2 b m m -1 2 k 4 b m -1 2 k -1 -1 b m -1 2 k 1 2 Erfi -1 c p -1 2 b m -1 2 k z 2 -1 b m -1 2 k 1 2 -1 c p 2 -1 2 b m m -1 2 k 4 b m -1 2 k -1 b m -1 2 k 1 2 Erfi c p 2 b m -1 2 k z 2 b m -1 2 k 1 2 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18