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/01.20.21.3969.01

 Input Form

 Integrate[z^n E^(p z) Cos[d + c z] Cosh[b + a z]^\[Nu], z] == ((1/2) n! Cosh[b + a z]^\[Nu] (E^((-I) d + ((-I) c + p) z) Sum[(1/(-j + n)!) ((-1)^j z^(-j + n) ((-I) c + p - a \[Nu])^(-1 - j) HypergeometricPFQ[{Subscript[b, 1], \[Ellipsis], Subscript[b, 1 + j], -\[Nu]}, {1 + Subscript[b, 1], \[Ellipsis], 1 + Subscript[b, 1 + j]}, -E^(2 (b + a z))]), {j, 0, n}] + E^(I d + (I c + p) z) Sum[(1/(-j + n)!) ((-1)^j z^(-j + n) (I c + p - a \[Nu])^(-1 - j) HypergeometricPFQ[{Subscript[c, 1], \[Ellipsis], Subscript[c, 1 + j], -\[Nu]}, {1 + Subscript[c, 1], \[Ellipsis], 1 + Subscript[c, 1 + j]}, -E^(2 (b + a z))]), {j, 0, n}]))/(1 + E^(2 (b + a z)))^\[Nu] /; Subscript[b, 1] == Subscript[b, 2] == \[Ellipsis] == Subscript[b, n + 1] == (p - I c - a \[Nu])/(2 a) && Subscript[c, 1] == Subscript[c, 2] == \[Ellipsis] == Subscript[c, n + 1] == (p + I c - a \[Nu])/(2 a) && Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n p z cos ( d + c z ) cosh ν ( b + a z ) z 1 2 ( 1 + 2 ( b + a z ) ) - ν n ! cosh ν ( b + a z ) ( - d + ( - c + p ) z j = 0 n ( - 1 ) j z n - j ( - c + p - a ν ) - j - 1 ( n - j ) ! j + 2 F j + 1 ( - c + p - a ν 2 a , , - c + p - a ν 2 a , - ν ; - c + p - a ν 2 a + 1 , , - c + p - a ν 2 a + 1 ; - 2 ( b + a z ) ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox[RowBox[List["j", "+", "2"]], TraditionalForm]], SubscriptBox["F", FormBox[RowBox[List["j", "+", "1"]], TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "c"]], "+", "p", "-", RowBox[List["a", " ", "\[Nu]"]]]], RowBox[List["2", " ", "a"]]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "c"]], "+", "p", "-", RowBox[List["a", " ", "\[Nu]"]]]], RowBox[List["2", " ", "a"]]], HypergeometricPFQ], ",", TagBox[RowBox[List["-", "\[Nu]"]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "c"]], "+", "p", "-", RowBox[List["a", " ", "\[Nu]"]]]], RowBox[List["2", " ", "a"]]], "+", "1"]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "c"]], "+", "p", "-", RowBox[List["a", " ", "\[Nu]"]]]], RowBox[List["2", " ", "a"]]], "+", "1"]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]]]]], HypergeometricPFQ]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], HypergeometricPFQ] + d + ( c + p ) z j = 0 n ( - 1 ) j z n - j ( c + p - a ν ) - j - 1 ( n - j ) ! j + 2 F j + 1 ( c + p - a ν 2 a , , c + p - a ν 2 a , - ν ; c + p - a ν 2 a + 1 , , c + p - a ν 2 a + 1 ; - 2 ( b + a z ) ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox[RowBox[List["j", "+", "2"]], TraditionalForm]], SubscriptBox["F", FormBox[RowBox[List["j", "+", "1"]], TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", "p", "-", RowBox[List["a", " ", "\[Nu]"]]]], RowBox[List["2", " ", "a"]]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", "p", "-", RowBox[List["a", " ", "\[Nu]"]]]], RowBox[List["2", " ", "a"]]], HypergeometricPFQ], ",", TagBox[RowBox[List["-", "\[Nu]"]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", "p", "-", RowBox[List["a", " ", "\[Nu]"]]]], RowBox[List["2", " ", "a"]]], "+", "1"]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", "p", "-", RowBox[List["a", " ", "\[Nu]"]]]], RowBox[List["2", " ", "a"]]], "+", "1"]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]]]]], HypergeometricPFQ]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], HypergeometricPFQ] ) /; n Condition z z n p z d c z b a z ν 1 2 1 2 b a z -1 ν n b a z ν -1 d -1 c p z j 0 n -1 j z n -1 j -1 c p -1 a ν -1 j -1 n -1 j -1 HypergeometricPFQ -1 c p -1 a ν 2 a -1 -1 c p -1 a ν 2 a -1 -1 ν -1 c p -1 a ν 2 a -1 1 -1 c p -1 a ν 2 a -1 1 -1 2 b a z d c p z j 0 n -1 j z n -1 j c p -1 a ν -1 j -1 n -1 j -1 HypergeometricPFQ c p -1 a ν 2 a -1 c p -1 a ν 2 a -1 -1 ν c p -1 a ν 2 a -1 1 c p -1 a ν 2 a -1 1 -1 2 b a z n [/itex]

 Rule Form

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

 2002-12-18