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/01.20.21.1337.01

 Input Form

 Integrate[E^(p z) Cosh[d z] (a Sin[e z] + b Cos[e z])^\[Beta], z] == (1/2) (-((1/(d - p + I e \[Beta])) ((E^((-d + p) z) (((-I) a (-1 + E^(2 I e z)) + b (1 + E^(2 I e z)))/ E^(I e z))^\[Beta] Hypergeometric2F1[-((I (-d + p - I e \[Beta]))/ (2 e)), -\[Beta], (1/2) (2 - (I (-d + p))/e - \[Beta]), (((-I) a + b) E^(2 I e z))/((-I) a - b)])/ (2^\[Beta] (1 + (((-I) a + b) E^(2 I e z))/(I a + b))^\[Beta]))) - (1/(-d - p + I e \[Beta])) ((E^((d + p) z) (((-I) a (-1 + E^(2 I e z)) + b (1 + E^(2 I e z)))/ E^(I e z))^\[Beta] Hypergeometric2F1[ -((I (d + p - I e \[Beta]))/(2 e)), -\[Beta], (1/2) (2 - (I (d + p))/e - \[Beta]), (((-I) a + b) E^(2 I e z))/ ((-I) a - b)])/(2^\[Beta] (1 + (((-I) a + b) E^(2 I e z))/(I a + b))^ \[Beta])))

 Standard Form

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 MathML Form

 p z cosh ( d z ) ( a sin ( e z ) + b cos ( e z ) ) β z 1 2 ( - 1 d - p + e β ( 2 - β ( p - d ) z ( 2 e z ( b - a ) b + a + 1 ) - β ( - e z ( b ( 1 + 2 e z ) - a ( - 1 + 2 e z ) ) ) β 2 F 1 ( - ( - d + p - e β ) 2 e , - β ; 1 2 ( - ( p - d ) e - β + 2 ) ; ( b - a ) 2 e z - b - a ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", "p", "-", RowBox[List["\[ImaginaryI]", " ", "e", " ", "\[Beta]"]]]], ")"]]]], RowBox[List["2", " ", "e"]]]]], Hypergeometric2F1], ",", TagBox[RowBox[List["-", "\[Beta]"]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "-", "d"]], ")"]]]], "e"]]], "-", "\[Beta]", "+", "2"]], ")"]]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "a"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["\[ImaginaryI]", " ", "a", " "]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) - 1 - d - p + e β ( 2 - β ( d + p ) z ( 2 e z ( b - a ) b + a + 1 ) - β ( - e z ( b ( 1 + 2 e z ) - a ( - 1 + 2 e z ) ) ) β 2 F 1 ( - ( d + p - e β ) 2 e , - β ; 1 2 ( - ( d + p ) e - β + 2 ) ; ( b - a ) 2 e z - b - a ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", "p", "-", RowBox[List["\[ImaginaryI]", " ", "e", " ", "\[Beta]"]]]], ")"]]]], RowBox[List["2", " ", "e"]]]]], Hypergeometric2F1], ",", TagBox[RowBox[List["-", "\[Beta]"]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]]]], "e"]]], "-", "\[Beta]", "+", "2"]], ")"]]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "a"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["\[ImaginaryI]", " ", "a", " "]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) ) z p z d z a e z b e z β 1 2 -1 1 d -1 p e β -1 2 -1 β p -1 d z 2 e z b -1 a b a -1 1 -1 β -1 e z b 1 2 e z -1 a -1 2 e z β Hypergeometric2F1 -1 -1 d p -1 e β 2 e -1 -1 β 1 2 -1 p -1 d e -1 -1 β 2 b -1 a 2 e z -1 b -1 a -1 -1 1 -1 d -1 p e β -1 2 -1 β d p z 2 e z b -1 a b a -1 1 -1 β -1 e z b 1 2 e z -1 a -1 2 e z β Hypergeometric2F1 -1 d p -1 e β 2 e -1 -1 β 1 2 -1 d p e -1 -1 β 2 b -1 a 2 e z -1 b -1 a -1 [/itex]

 Rule Form

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

 2002-12-18