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/01.23.21.0288.01

 Input Form

 Integrate[z^n E^(p z) Cos[a z]^m Cosh[b z]^u Csch[c z], z] == (-2^(1 - m - u)) E^((c + p) z) Binomial[m, m/2] Binomial[u, u/2] n! (1 - Mod[m, 2]) (1 - Mod[u, 2]) Sum[(1/(-j + n)!) ((-1)^j (c + p)^(-1 - j) z^(-j + n) 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 - u) Binomial[u, u/2] n! (1 - Mod[u, 2]) Sum[Binomial[m, k] (E^((c - I a (-2 k + m) + p) z) Sum[(1/(-j + n)!) ((-1)^j (c - I a (-2 k + m) + p)^(-1 - j) z^(-j + n) 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^((c + I a (-2 k + m) + p) z) Sum[(1/(-j + n)!) ((-1)^j (c + I a (-2 k + m) + p)^(-1 - j) z^(-j + n) 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)]}] - 2^(1 - m - u) Binomial[m, m/2] n! (1 - Mod[m, 2]) Sum[Binomial[u, s] (E^((c + p - b (-2 s + u)) z) Sum[(1/(-j + n)!) ((-1)^j (c + p - b (-2 s + u))^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[d, 1], \[Ellipsis], Subscript[d, j + 1], 1}, {1 + Subscript[d, 1], \[Ellipsis], 1 + Subscript[d, j + 1]}, E^(2 c z)]), {j, 0, n}] + E^((c + p + b (-2 s + u)) z) Sum[(1/(-j + n)!) ((-1)^j (c + p + b (-2 s + u))^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[e, 1], \[Ellipsis], Subscript[e, j + 1], 1}, {1 + Subscript[e, 1], \[Ellipsis], 1 + Subscript[e, j + 1]}, E^(2 c z)]), {j, 0, n}]), {s, 0, Floor[(1/2) (-1 + u)]}] - 2^(1 - m - u) n! Sum[Binomial[m, k] Sum[Binomial[u, s] (E^((c - I a (-2 k + m) + p - b (-2 s + u)) z) Sum[(1/(-j + n)!) ((-1)^j (c - I a (-2 k + m) + p - b (-2 s + u))^ (-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[f, 1], \[Ellipsis], Subscript[f, j + 1], 1}, {1 + Subscript[f, 1], \[Ellipsis], 1 + Subscript[f, j + 1]}, E^(2 c z)]), {j, 0, n}] + E^((c + I a (-2 k + m) + p - b (-2 s + u)) z) Sum[(1/(-j + n)!) ((-1)^j (c + I a (-2 k + m) + p - b (-2 s + u))^ (-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[g, 1], \[Ellipsis], Subscript[g, j + 1], 1}, {1 + Subscript[g, 1], \[Ellipsis], 1 + Subscript[g, j + 1]}, E^(2 c z)]), {j, 0, n}] + E^((c - I a (-2 k + m) + p + b (-2 s + u)) z) Sum[(1/(-j + n)!) ((-1)^j (c - I a (-2 k + m) + p + b (-2 s + u))^ (-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[h, 1], \[Ellipsis], Subscript[h, j + 1], 1}, {1 + Subscript[h, 1], \[Ellipsis], 1 + Subscript[h, j + 1]}, E^(2 c z)]), {j, 0, n}] + E^((c + I a (-2 k + m) + p + b (-2 s + u)) z) Sum[(1/(-j + n)!) ((-1)^j (c + I a (-2 k + m) + p + b (-2 s + u))^ (-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[q, 1], \[Ellipsis], Subscript[q, j + 1], 1}, {1 + Subscript[q, 1], \[Ellipsis], 1 + Subscript[q, j + 1]}, E^(2 c z)]), {j, 0, n}]), {s, 0, Floor[(1/2) (-1 + u)]}], {k, 0, Floor[(1/2) (-1 + m)]}] /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n + 1] == (c + p)/(2 c) && Subscript[b, 1] == Subscript[b, 2] == \[Ellipsis] == Subscript[b, n + 1] == ((-I) a (-2 k + m) + p + c)/(2 c) && Subscript[c, 1] == Subscript[c, 2] == \[Ellipsis] == Subscript[c, n + 1] == (I a (-2 k + m) + p + c)/(2 c) && Subscript[d, 1] == Subscript[d, 2] == \[Ellipsis] == Subscript[d, n + 1] == (p - b (-2 s + u) + c)/(2 c) && Subscript[e, 1] == Subscript[e, 2] == \[Ellipsis] == Subscript[e, n + 1] == (p + b (-2 s + u) + c)/(2 c) && Subscript[f, 1] == Subscript[f, 2] == \[Ellipsis] == Subscript[f, n + 1] == ((-I) a (-2 k + m) + p - b (-2 s + u) + c)/(2 c) && Subscript[g, 1] == Subscript[g, 2] == \[Ellipsis] == Subscript[g, n + 1] == (I a (-2 k + m) + p - b (-2 s + u) + c)/(2 c) && Subscript[h, 1] == Subscript[h, 2] == \[Ellipsis] == Subscript[h, n + 1] == ((-I) a (-2 k + m) + p + b (-2 s + u) + c)/(2 c) && Subscript[q, 1] == Subscript[q, 2] == \[Ellipsis] == Subscript[q, n + 1] == (I a (-2 k + m) + p + b (-2 s + u) + c)/(2 c) && Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0 && Element[u, Integers] && u > 0

 Standard Form

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 MathML Form

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k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] s = 0 u - 1 2 ( u s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity, Rule[Editable, True]]], List[TagBox["s", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( ( c - a ( m - 2 k ) + p - b ( u - 2 s ) ) z j = 0 n ( - 1 ) j ( c - a ( m - 2 k ) + p - b ( u - 2 s ) ) - j - 1 z n - j ( n - j ) ! j + 2 F j + 1 ( c - a ( m - 2 k ) + p - b ( u - 2 s ) 2 c , , c - a ( m - 2 k ) + p - b ( u - 2 s ) 2 c , 1 ; c - a ( m - 2 k ) + p - b ( u - 2 s ) 2 c + 1 , , c - a ( m - 2 k ) + p - b ( u - 2 s ) 2 c + 1 ; 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[RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "-", RowBox[List["b", " ", RowBox[List["(", RowBox[List["u", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox[RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "-", RowBox[List["b", " ", RowBox[List["(", RowBox[List["u", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox["1", HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "-", RowBox[List["b", " ", RowBox[List["(", RowBox[List["u", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], RowBox[List["2", " ", "c"]]], "+", "1"]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[RowBox[List[FractionBox[RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "-", RowBox[List["b", " ", RowBox[List["(", RowBox[List["u", "-", 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 + a ( m - 2 k ) + p - b ( u - 2 s ) ) z j = 0 n ( - 1 ) j ( c + a ( m - 2 k ) + p - b ( u - 2 s ) ) - j - 1 z n - j ( n - j ) ! 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 Rule Form

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

 2002-12-18