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 Cot

 http://functions.wolfram.com/01.09.21.0250.01

 Input Form

 Integrate[(Cot[t] - 1/t) (z - t)^n, {t, 0, z}] == z^n (Log[Sin[z]] - Log[z]) - (I n z^(1 + n))/(1 + n) - z^n Sum[((-1)^(n - j) Binomial[n, j])/(n - j), {j, 0, n - 1}] - Sum[(-1)^(n - j) Binomial[n, j] z^j Sum[(Binomial[n - j, k] k! z^(n - j - k) PolyLog[k + 1, E^(-2 I z)])/ (2 I)^k, {k, 0, n - j}], {j, 0, n - 1}] + Sum[Binomial[n, j] (-2 I)^(j - n) (n - j)! z^j PolyLog[1 + n - j, 1], {j, 0, n - 1}] /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 0 z ( cot ( t ) - 1 t ) ( z - t ) n t ( log ( sin ( z ) ) - log ( z ) ) z n - ( j = 0 n - 1 ( - 1 ) n - j ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox["j", Identity, Rule[Editable, True], Rule[Selectable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] n - j ) z n - n z n + 1 n + 1 + j = 0 n - 1 ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox["j", Identity, Rule[Editable, True], Rule[Selectable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] ( - 2 ) j - n ( n - j ) ! z j Li PolyLog - j + n + 1 ( 1 ) - j = 0 n - 1 ( - 1 ) n - j ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox["j", Identity, Rule[Editable, True], Rule[Selectable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] z j k = 0 n - j ( n - j k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List["n", "-", "j"]], Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox["k", Identity, Rule[Editable, True], Rule[Selectable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] k ! ( 2 ) - k z - j - k + n Li PolyLog k + 1 ( - 2 z ) /; n TagBox["\[DoubleStruckCapitalN]", Function[List[], Integers]] Condition t 0 z t -1 1 t -1 z -1 t n z -1 z z n -1 j 0 n -1 -1 n -1 j Binomial n j n -1 j -1 z n -1 n z n 1 n 1 -1 j 0 n -1 Binomial n j -2 j -1 n n -1 j z j PolyLog -1 j n 1 1 -1 j 0 n -1 -1 n -1 j Binomial n j z j k 0 n -1 j Binomial n -1 j k k 2 -1 k z -1 j -1 k n PolyLog k 1 -2 z n [/itex]

 Rule Form

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

 2007-05-02