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 Cos

 http://functions.wolfram.com/01.07.21.2615.01

 Input Form

 Integrate[E^(p z) Sin[d + c z]^m Cos[a z]^\[Nu], z] == (-((1/(p - I a \[Nu])) ((E^(p z) Binomial[m, m/2] Cos[a z]^\[Nu] Hypergeometric2F1[-((I (p - I a \[Nu]))/(2 a)), -\[Nu], (1/2) (2 - (I p)/a - \[Nu]), -E^(2 I a z)] (-1 + Mod[m, 2]))/ (1 + E^(2 I a z))^\[Nu])) + (Cos[a z]^\[Nu] Sum[(-1)^k E^(I d (-2 k + m)) Binomial[m, k] ((E^(I (4 d k - 2 d m + m Pi + 2 c k z - c m z - I p z)) Hypergeometric2F1[(I (2 I c k - I c m + p + I a \[Nu]))/(2 a), -\[Nu], (I (2 I c k - I c m + p + I a (-2 + \[Nu])))/(2 a), -E^(-2 I a z)])/(I c (2 k - m) + p + I a \[Nu]) + (E^((I c (-2 k + m) + p) z) Hypergeometric2F1[ (I (I c (-2 k + m) + p + I a \[Nu]))/(2 a), -\[Nu], (I (-2 I c k + I c m + p + I a (-2 + \[Nu])))/(2 a), -E^(-2 I a z)])/(I c (-2 k + m) + p + I a \[Nu])), {k, 0, Floor[(1/2) (-1 + m)]}])/(I^m (1 + E^(-2 I a z))^\[Nu]))/2^m /; Element[m, Integers] && m > 0

 Standard Form

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"\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

 p z sin m ( d + c z ) cos ν ( a z ) z 2 - m ( - 1 p - a ν ( p z ( 1 + 2 a z ) - ν ( 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]]]]] cos ν ( a z ) 2 F 1 ( - ( p - a ν ) 2 a , - ν ; 1 2 ( - p a - ν + 2 ) ; - 2 a z ) 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["p", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "\[Nu]"]]]], ")"]]]], RowBox[List["2", " ", "a"]]]]], Hypergeometric2F1], ",", TagBox[RowBox[List["-", "\[Nu]"]], 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]", " ", "p"]], "a"]]], "-", "\[Nu]", "+", "2"]], ")"]]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ( m mod 2 \$CellContext`m 2 - 1 ) ) + - m ( 1 + - 2 a z ) - ν cos ν ( a z ) k = 0 m - 1 2 ( - 1 ) k d ( m - 2 k ) ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( ( 4 d k + 2 c z k - 2 d m - c m z - p z + m π ) 2 F 1 ( ( 2 c k - c m + p + a ν ) 2 a , - ν ; ( 2 c k - c m + p + a ( ν - 2 ) ) 2 a ; - - 2 a z ) 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[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "m"]], "+", "p", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", "\[Nu]"]]]], ")"]]]], RowBox[List["2", " ", "a"]]], Hypergeometric2F1], ",", TagBox[RowBox[List["-", "\[Nu]"]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "m"]], "+", "p", "+", RowBox[List["a", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["\[Nu]", "-", "2"]], ")"]]]]]], ")"]]]], RowBox[List["2", " ", "a"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "a", " ", "z"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) / ( c ( 2 k - m ) + p + a ν ) + ( ( c ( m - 2 k ) + p ) z 2 F 1 ( ( c ( m - 2 k ) + p + a ν ) 2 a , - ν ; ( - 2 c k + c m + p + a ( ν - 2 ) ) 2 a ; - - 2 a z ) 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[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["c", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", "\[Nu]"]]]], ")"]]]], RowBox[List["2", " ", "a"]]], Hypergeometric2F1], ",", TagBox[RowBox[List["-", "\[Nu]"]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "\[ImaginaryI]", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "m"]], "+", "p", "+", RowBox[List["a", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["\[Nu]", "-", "2"]], ")"]]]]]], ")"]]]], RowBox[List["2", " ", "a"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "a", " ", "z"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) / ( c ( m - 2 k ) + p + a ν ) ) ) /; m + Condition z p z d c z m a z ν 2 -1 m -1 1 p -1 a ν -1 p z 1 2 a z -1 ν Binomial m m 2 -1 a z ν Hypergeometric2F1 -1 p -1 a ν 2 a -1 -1 ν 1 2 -1 p a -1 -1 ν 2 -1 2 a z \$CellContext`m 2 -1 -1 m 1 -2 a z -1 ν a z ν k 0 m -1 2 -1 -1 k d m -1 2 k Binomial m k 4 d k 2 c z k -1 2 d m -1 c m z -1 p z m Hypergeometric2F1 2 c k -1 c m p a ν 2 a -1 -1 ν 2 c k -1 c m p a ν -2 2 a -1 -1 -2 a z c 2 k -1 m p a ν -1 c m -1 2 k p z Hypergeometric2F1 c m -1 2 k p a ν 2 a -1 -1 ν -2 c k c m p a ν -2 2 a -1 -1 -2 a z c m -1 2 k p a ν -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18