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/01.20.21.1289.01

 Input Form

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

 Standard Form

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 MathML Form

 p z 2 cos m ( b z 2 ) cosh ( c z ) z 2 - m - 2 π ( 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]]]]] ( - c 2 4 p erfi ( 2 p z - c 2 p ) + - c 2 4 p erfi ( c + 2 p z 2 p ) ) ( 1 - m mod 2 \$CellContext`m 2 ) p + 2 - m - 2 π 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]]]]] ( ( - c 2 4 ( - b m + p + 2 b s ) - b m + p + 2 b s ( b m + p - 2 b s ) erfi ( 2 ( - b m + p + 2 b s ) z - c 2 - b m + p + 2 b s ) + - c 2 4 ( b m + p - 2 b s ) ( - b m + p + 2 b s ) b m + p - 2 b s erfi ( c + 2 p z - 2 ( 2 b s - b m ) z 2 b m + p - 2 b s ) ) / ( ( b m + p - 2 b s ) ( - b m + p + 2 b s ) ) + ( - c 2 4 ( - b m + p + 2 b s ) - b m + p + 2 b s ( b m + p - 2 b s ) erfi ( c + 2 p z - 2 ( b m - 2 b s ) z 2 - b m + p + 2 b s ) + - c 2 4 ( b m + p - 2 b s ) ( - b m + p + 2 b s ) b m + p - 2 b s erfi ( 2 ( b m + p - 2 b s ) z - c 2 b m + p - 2 b s ) ) / ( ( b m + p - 2 b s ) ( - b m + p + 2 b s ) ) ) /; m TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] m > 0 Condition z p z 2 b z 2 m c z 2 -1 m -2 1 2 Binomial m m 2 -1 -1 c 2 4 p -1 Erfi 2 p z -1 c 2 p 1 2 -1 -1 c 2 4 p -1 Erfi c 2 p z 2 p 1 2 -1 1 -1 \$CellContext`m 2 p 1 2 -1 2 -1 m -2 1 2 s 0 m -1 2 -1 Binomial m s -1 c 2 4 -1 b m p 2 b s -1 -1 b m p 2 b s 1 2 b m p -1 2 b s Erfi 2 -1 b m p 2 b s z -1 c 2 -1 b m p 2 b s 1 2 -1 -1 c 2 4 b m p -1 2 b s -1 -1 b m p 2 b s b m p -1 2 b s 1 2 Erfi c 2 p z -1 2 2 b s -1 b m z 2 b m p -1 2 b s 1 2 -1 b m p -1 2 b s -1 b m p 2 b s -1 -1 c 2 4 -1 b m p 2 b s -1 -1 b m p 2 b s 1 2 b m p -1 2 b s Erfi c 2 p z -1 2 b m -1 2 b s z 2 -1 b m p 2 b s 1 2 -1 -1 c 2 4 b m p -1 2 b s -1 -1 b m p 2 b s b m p -1 2 b s 1 2 Erfi 2 b m p -1 2 b s z -1 c 2 b m p -1 2 b s 1 2 -1 b m p -1 2 b s -1 b m p 2 b s -1 m m 0 [/itex]

 Rule Form

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

 2002-12-18