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 Csch

 http://functions.wolfram.com/01.23.21.0060.01

 Input Form

 Integrate[E^(p z) Sin[b z]^m Csch[c z], z] == 2^(1 - m) E^((c + p) z) Binomial[m, m/2] (-1 + Mod[m, 2]) (HypergeometricPFQ[{(p + c)/(2 c), 1}, {1 + (p + c)/(2 c)}, E^(2 c z)]/ (p + c)) - 2^(1 - m) E^(c z) Sum[(-1)^s Binomial[m, s] ((E^((-(1/2)) I m Pi + (p + I b (m - 2 s)) z) HypergeometricPFQ[ {(I b (m - 2 s) + p + c)/(2 c), 1}, {1 + (I b (m - 2 s) + p + c)/(2 c)}, E^(2 c z)])/ (p + I b (m - 2 s) + c) + (E^((I m Pi)/2 + (p - I b (m - 2 s)) z) HypergeometricPFQ[{(p - I b (m - 2 s) + c)/(2 c), 1}, {1 + (p - I b (m - 2 s) + c)/(2 c)}, E^(2 c z)])/ (p - I b (m - 2 s) + c)), {s, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18