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; }

 Csch

 http://functions.wolfram.com/01.23.21.0053.01

 Input Form

 Integrate[z^n Sin[b z]^m Csch[c z], z] == 2^(1 - m) E^(c z) Binomial[m, m/2] n! (-1 + Mod[m, 2]) Sum[(1/(-j + n)!) (-1)^j z^(-j + n) c^(-1 - j) HypergeometricPFQ[ {Subscript[a, 1], \[Ellipsis], Subscript[a, j + 1], 1}, {1 + Subscript[a, 1], \[Ellipsis], 1 + Subscript[a, j + 1]}, E^(2 c z)], {j, 0, n}] - 2^(1 - m) E^(c z) n! Sum[(-1)^k Binomial[m, k] (E^((-(1/2)) I m Pi + I b (-2 k + m) z) Sum[(1/(-j + n)!) (-1)^j z^(-j + n) (I b (-2 k + m) + c)^(-1 - j) HypergeometricPFQ[{Subscript[b, 1], \[Ellipsis], Subscript[b, j + 1], 1}, {1 + Subscript[b, 1], \[Ellipsis], 1 + Subscript[b, j + 1]}, E^(2 c z)], {j, 0, n}] + E^((I m Pi)/2 - I b (-2 k + m) z) Sum[(1/(-j + n)!) (-1)^j z^(-j + n) ((-I) b (-2 k + m) + c)^(-1 - j) HypergeometricPFQ[ {Subscript[c, 1], \[Ellipsis], Subscript[c, j + 1], 1}, {1 + Subscript[c, 1], \[Ellipsis], 1 + Subscript[c, j + 1]}, E^(2 c z)], {j, 0, n}]), {k, 0, Floor[(1/2) (-1 + m)]}] /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n + 1] == 1/2 && Subscript[b, 1] == Subscript[b, 2] == \[Ellipsis] == Subscript[b, n + 1] == (c + I b (-2 k + m))/(2 c) && Subscript[c, 1] == Subscript[c, 2] == \[Ellipsis] == Subscript[c, n + 1] == (c - I b (-2 k + m))/(2 c) && Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 z n sin m ( b z ) csch ( c z ) z 2 1 - m 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]]]]] n ! ( m mod 2 \$CellContext`m 2 - 1 ) j = 0 n 1 ( n - j ) ! ( - 1 ) j z n - j c - j - 1 j + 2 F j + 1 ( 1 2 , , 1 2 , 1 ; 3 2 , , 3 2 ; 2 c 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["1", "2"], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQ], ",", TagBox["1", HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "2"], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox["3", "2"], 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 n ! 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]]]]] ( b ( m - 2 k ) z - m π 2 j = 0 n 1 ( n - j ) ! 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 Rule Form

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

 2002-12-18