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 Csch

 http://functions.wolfram.com/01.23.21.0209.01

 Input Form

 Integrate[Sin[a z]^m Cosh[c z]^\[Mu] Csch[c z], z] == (1/(c (\[Mu] - 1))) ((2^(1 - m) AppellF1[(1 - \[Mu])/2, -\[Mu], 1, (3 - \[Mu])/2, -E^(-2 c z), E^(-2 c z)] Binomial[m, m/2] Cosh[c z]^\[Mu] (1 - Mod[m, 2]))/(E^(c z) (1 + E^(-2 c z))^\[Mu])) + (2^(1 - m) Cosh[c z]^\[Mu] Sum[(-1)^k ((E^((I m Pi)/2 + I a (2 k - m) z) AppellF1[-((I a (2 k - m) + c \[Mu] - c)/(2 c)), -\[Mu], 1, ((-I) a (2 k - m) + c (3 - \[Mu]))/(2 c), -E^(-2 c z), E^(-2 c z)])/(I a (2 k - m) + c (\[Mu] - 1)) + (E^((-(1/2)) I m Pi + I a (-2 k + m) z) AppellF1[ -((I a (-2 k + m) + c \[Mu] - c)/(2 c)), -\[Mu], 1, ((-I) a (-2 k + m) + c (3 - \[Mu]))/(2 c), -E^(-2 c z), E^(-2 c z)])/(I a (-2 k + m) + c (\[Mu] - 1))) Binomial[m, k], {k, 0, Floor[(1/2) (-1 + m)]}])/(E^(c z) (1 + E^(-2 c z))^\[Mu]) /; Element[m, Integers] && m > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]], "m"], SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], "\[Mu]"], RowBox[List["Csch", "[", RowBox[List["c", " ", "z"]], "]"]], " ", RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["c", " ", RowBox[List["(", RowBox[List["\[Mu]", "-", "1"]], ")"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "m"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "c"]], " ", "z"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "z"]]]]], ")"]], RowBox[List["-", "\[Mu]"]]], " ", RowBox[List["AppellF1", "[", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Mu]"]], "2"], ",", RowBox[List["-", "\[Mu]"]], ",", "1", ",", 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"z"]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List["\[Mu]", "-", "1"]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

 sin m ( a z ) cosh μ ( c z ) csch ( c z ) z 2 1 - m - c z cosh μ ( c z ) ( 1 + - 2 c z ) - μ k = 0 m - 1 2 ( - 1 ) k ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( π m 2 + a ( 2 k - m ) z F 1 AppellF1 ( - μ c - c + a ( 2 k - m ) 2 c ; - μ , 1 ; c ( 3 - μ ) - a ( 2 k - m ) 2 c ; - - 2 c z , - 2 c z ) ( μ - 1 ) c + a ( 2 k - m ) + a ( m - 2 k ) z - m π 2 F 1 AppellF1 ( - μ c - c + a ( m - 2 k ) 2 c ; - μ , 1 ; c ( 3 - μ ) - a ( m - 2 k ) 2 c ; - - 2 c z , - 2 c z ) ( μ - 1 ) c + a ( m - 2 k ) ) + 1 c ( μ - 1 ) 2 1 - m - c z ( 1 + - 2 c z ) - μ F 1 AppellF1 ( 1 - μ 2 ; - μ , 1 ; 3 - μ 2 ; - - 2 c z , - 2 c z ) ( 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]]]]] cosh μ ( c z ) ( 1 - m mod 2 \$CellContext`m 2 ) /; m + Condition z a z m c z μ c z 2 1 -1 m -1 c z c z μ 1 -2 c z -1 μ k 0 m -1 2 -1 -1 k Binomial m k m 2 -1 a 2 k -1 m z AppellF1 -1 μ c -1 c a 2 k -1 m 2 c -1 -1 μ 1 c 3 -1 μ -1 a 2 k -1 m 2 c -1 -1 -2 c z -2 c z μ -1 c a 2 k -1 m -1 a m -1 2 k z -1 m 2 -1 AppellF1 -1 μ c -1 c a m -1 2 k 2 c -1 -1 μ 1 c 3 -1 μ -1 a m -1 2 k 2 c -1 -1 -2 c z -2 c z μ -1 c a m -1 2 k -1 1 c μ -1 -1 2 1 -1 m -1 c z 1 -2 c z -1 μ AppellF1 1 -1 μ 2 -1 -1 μ 1 3 -1 μ 2 -1 -1 -2 c z -2 c z Binomial m m 2 -1 c z μ 1 -1 \$CellContext`m 2 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18