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/01.20.21.3985.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18