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 Csch

 http://functions.wolfram.com/01.23.21.0294.01

 Input Form

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

 z n p z cos m ( a z ) coth u ( c z ) csch ( c z ) z 2 - m - u ( 1 - 2 c z ) u + 1 ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["m", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] n ! 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j + 2 F j + 1 ( p + c ( 2 s + 1 ) 2 c , , p + c ( 2 s + 1 ) 2 c , u + 1 ; p + c ( 2 s + 1 ) 2 c + 1 , , p + c ( 2 s + 1 ) 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["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox[RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], "+", "1"]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[RowBox[List[FractionBox[RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "+", "1"]], ")"]]]]]], 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] + ( p + c ( u - 2 s ) ) z j = 0 n ( - 1 ) j ( p + c ( - 2 s + 2 u + 1 ) ) - j - 1 z n - j ( n - j ) ! j + 2 F j + 1 ( p + c ( - 2 s + 2 u + 1 ) 2 c , , p + c ( - 2 s + 2 u + 1 ) 2 c , u + 1 ; p + c ( - 2 s + 2 u + 1 ) 2 c + 1 , , p + c ( - 2 s + 2 u + 1 ) 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["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", RowBox[List["2", " ", "u"]], "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox[RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", RowBox[List["2", " ", "u"]], "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", RowBox[List["2", " ", "u"]], "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], "+", "1"]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[RowBox[List[FractionBox[RowBox[List["p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", RowBox[List["2", " ", "u"]], "+", "1"]], ")"]]]]]], 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] ) ) csch u + 1 ( c z ) + 2 - m - u ( 1 - 2 c z ) u + 1 n ! ( 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]] ( ( p - a ( m - 2 k ) ) z ( u u 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["u", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 1 - u mod 2 \$CellContext`u 2 ) j = 0 n ( - 1 ) j ( - a ( m - 2 k ) + p + c ( u + 1 ) ) - j - 1 z n - j ( n - j ) ! j + 2 F j + 1 ( - a ( m - 2 k ) + p + c ( u + 1 ) 2 c , , - a ( m - 2 k ) + p + c ( u + 1 ) 2 c , u + 1 ; - a ( m - 2 k ) + p + c ( u + 1 ) 2 c + 1 , , - a ( m - 2 k ) + p + c ( u + 1 ) 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[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List["u", "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List["u", "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List["u", "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], "+", "1"]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List["u", "+", "1"]], ")"]]]]]], 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] + ( a ( m - 2 k ) + p ) z ( u u 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["u", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 1 - u mod 2 \$CellContext`u 2 ) j = 0 n ( - 1 ) j ( a ( m - 2 k ) + p + c ( u + 1 ) ) - j - 1 z n - j ( n - j ) ! j + 2 F j + 1 ( a ( m - 2 k ) + p + c ( u + 1 ) 2 c , , a ( m - 2 k ) + p + c ( u + 1 ) 2 c , u + 1 ; a ( m - 2 k ) + p + c ( u + 1 ) 2 c + 1 , , a ( m - 2 k ) + p + c ( u + 1 ) 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[RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List["u", "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List["u", "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List["u", "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], "+", "1"]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List["u", "+", "1"]], ")"]]]]]], 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] + 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]] ( ( - a ( m - 2 k ) + p - c ( u - 2 s ) ) z j = 0 n ( - 1 ) j ( - a ( m - 2 k ) + p + c ( 2 s + 1 ) ) - j - 1 z n - j ( n - j ) ! j + 2 F j + 1 ( - a ( m - 2 k ) + p + c ( 2 s + 1 ) 2 c , , - a ( m - 2 k ) + p + c ( 2 s + 1 ) 2 c , u + 1 ; - a ( m - 2 k ) + p + c ( 2 s + 1 ) 2 c + 1 , , - a ( m - 2 k ) + p + c ( 2 s + 1 ) 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[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], "+", "1"]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "+", "1"]], ")"]]]]]], 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] + ( - a ( m - 2 k ) + p + c ( u - 2 s ) ) z j = 0 n ( - 1 ) j ( - a ( m - 2 k ) + p + c ( - 2 s + 2 u + 1 ) ) - j - 1 z n - j ( n - j ) ! j + 2 F j + 1 ( - a ( m - 2 k ) + p + c ( - 2 s + 2 u + 1 ) 2 c , , - a ( m - 2 k ) + p + c ( - 2 s + 2 u + 1 ) 2 c , u + 1 ; - a ( m - 2 k ) + p + c ( - 2 s + 2 u + 1 ) 2 c + 1 , , - a ( m - 2 k ) + p + c ( - 2 s + 2 u + 1 ) 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[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", RowBox[List["2", " ", "u"]], "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", RowBox[List["2", " ", "u"]], "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", RowBox[List["2", " ", "u"]], "+", "1"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], "+", "1"]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", RowBox[List["2", " ", "u"]], "+", "1"]], ")"]]]]]], 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] ) + 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]] ( ( a ( m - 2 k ) + p - c ( u - 2 s ) ) z j = 0 n ( - 1 ) j ( a ( m - 2 k ) + p + c ( 2 s + 1 ) ) - j - 1 z n - j ( n - j ) ! j + 2 F j + 1 ( a ( m - 2 k ) + p + c ( 2 s + 1 ) 2 c , , a ( m - 2 k ) + p + c ( 2 s + 1 ) 2 c , u + 1 ; 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n m + u + Condition z z n p z a z m c z u c z 2 -1 m -1 u 1 -1 2 c z u 1 Binomial m m 2 -1 n 1 -1 \$CellContext`m 2 p z Binomial u u 2 -1 1 -1 \$CellContext`u 2 j 0 n -1 j p c u 1 -1 j -1 z n -1 j n -1 j -1 HypergeometricPFQ p c u 1 2 c -1 p c u 1 2 c -1 u 1 p c u 1 2 c -1 1 p c u 1 2 c -1 1 2 c z s 0 u -1 2 -1 Binomial u s p -1 c u -1 2 s z j 0 n -1 j p c 2 s 1 -1 j -1 z n -1 j n -1 j -1 HypergeometricPFQ p c 2 s 1 2 c -1 p c 2 s 1 2 c -1 u 1 p c 2 s 1 2 c -1 1 p c 2 s 1 2 c -1 1 2 c z p c u -1 2 s z j 0 n -1 j p c -2 s 2 u 1 -1 j -1 z n -1 j n -1 j -1 HypergeometricPFQ p c -2 s 2 u 1 2 c -1 p c -2 s 2 u 1 2 c -1 u 1 p c -2 s 2 u 1 2 c -1 1 p c -2 s 2 u 1 2 c -1 1 2 c z c z u 1 2 -1 m -1 u 1 -1 2 c z u 1 n k 0 m -1 2 -1 Binomial m k p -1 a m -1 2 k z Binomial u u 2 -1 1 -1 \$CellContext`u 2 j 0 n -1 j -1 a m -1 2 k p c u 1 -1 j -1 z n -1 j n -1 j -1 HypergeometricPFQ -1 a m -1 2 k p c u 1 2 c -1 -1 a m -1 2 k p c u 1 2 c -1 u 1 -1 a m -1 2 k p c u 1 2 c -1 1 -1 a m -1 2 k p c u 1 2 c -1 1 2 c z a m -1 2 k p z Binomial u u 2 -1 1 -1 \$CellContext`u 2 j 0 n -1 j a m -1 2 k p c u 1 -1 j -1 z n -1 j n -1 j -1 HypergeometricPFQ a m -1 2 k p c u 1 2 c -1 a m -1 2 k p c u 1 2 c -1 u 1 a m -1 2 k p c u 1 2 c -1 1 a m -1 2 k p c u 1 2 c -1 1 2 c z s 0 u -1 2 -1 Binomial u s -1 a m -1 2 k p -1 c u -1 2 s z j 0 n -1 j -1 a m -1 2 k p c 2 s 1 -1 j -1 z n -1 j n -1 j -1 HypergeometricPFQ -1 a m -1 2 k p c 2 s 1 2 c -1 -1 a m -1 2 k p c 2 s 1 2 c -1 u 1 -1 a m -1 2 k p c 2 s 1 2 c -1 1 -1 a m -1 2 k p c 2 s 1 2 c -1 1 2 c z -1 a m -1 2 k p c u -1 2 s z j 0 n -1 j -1 a m -1 2 k p c -2 s 2 u 1 -1 j -1 z n -1 j n -1 j -1 HypergeometricPFQ -1 a m -1 2 k p c -2 s 2 u 1 2 c -1 -1 a m -1 2 k p c -2 s 2 u 1 2 c -1 u 1 -1 a m -1 2 k p c -2 s 2 u 1 2 c -1 1 -1 a m -1 2 k p c -2 s 2 u 1 2 c -1 1 2 c z s 0 u -1 2 -1 Binomial u s a m -1 2 k p -1 c u -1 2 s z j 0 n -1 j a m -1 2 k p c 2 s 1 -1 j -1 z n -1 j n -1 j -1 HypergeometricPFQ a m -1 2 k p c 2 s 1 2 c -1 a m -1 2 k p c 2 s 1 2 c -1 u 1 a m -1 2 k p c 2 s 1 2 c -1 1 a m -1 2 k p c 2 s 1 2 c -1 1 2 c z a m -1 2 k p c u -1 2 s z j 0 n -1 j a m -1 2 k p c -2 s 2 u 1 -1 j -1 z n -1 j n -1 j -1 HypergeometricPFQ a m -1 2 k p c -2 s 2 u 1 2 c -1 a m -1 2 k p c -2 s 2 u 1 2 c -1 u 1 a m -1 2 k p c -2 s 2 u 1 2 c -1 1 a m -1 2 k p c -2 s 2 u 1 2 c -1 1 2 c z c z u 1 n m SuperPlus u SuperPlus [/itex]

 Rule Form

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

 2002-12-18