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http://functions.wolfram.com/06.05.25.0007.01
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Residue[(Product[Gamma[Subscript[\[GothicCapitalA], k] s + Subscript[a, k]],
{k, 1, \[ScriptCapitalA]}] Product[Gamma[Subscript[b, k] -
Subscript[\[GothicCapitalB], k] s], {k, 1, \[ScriptCapitalB]}])/
(Product[Gamma[Subscript[\[GothicCapitalC], k] s + Subscript[c, k]],
{k, 1, \[ScriptCapitalC]}] Product[Gamma[Subscript[d, k] -
Subscript[\[GothicCapitalD], k] s], {k, 1, \[ScriptCapitalD]}])/z^s,
{s, (Subscript[b, 1] + l)/Subscript[\[GothicCapitalB], 1]}] ==
((-1)^(l - 1) Product[Gamma[Subscript[a, k] + Subscript[\[GothicCapitalA],
k] ((Subscript[b, 1] + l)/Subscript[\[GothicCapitalB], 1])]
Product[Gamma[Subscript[b, k] - Subscript[\[GothicCapitalB], k]
((Subscript[b, 1] + l)/Subscript[\[GothicCapitalB], 1])],
{k, 2, \[ScriptCapitalB]}], {k, 1, \[ScriptCapitalA]}])/
(Subscript[\[GothicCapitalB], 1] l!
Product[Gamma[Subscript[c, k] + Subscript[\[GothicCapitalC], k]
((Subscript[b, 1] + l)/Subscript[\[GothicCapitalB], 1])]
Product[Gamma[Subscript[d, k] - Subscript[\[GothicCapitalD], k]
((Subscript[b, 1] + l)/Subscript[\[GothicCapitalB], 1])],
{k, 1, \[ScriptCapitalD]}], {k, 1, \[ScriptCapitalC]}])/
z^((Subscript[b, 1] + l)/Subscript[\[GothicCapitalB], 1]) /;
Element[l, Integers] && l >= 0 &&
!Element[Subscript[b, j] - Subscript[\[GothicCapitalB], j]
((Subscript[b, 1] + l)/Subscript[\[GothicCapitalB], 1]), Integers] &&
2 <= j <= \[ScriptCapitalB] &&
!(Element[-Subscript[a, j] - Subscript[\[GothicCapitalA], j]
((Subscript[b, 1] + l)/Subscript[\[GothicCapitalB], 1]), Integers] &&
-Subscript[a, j] - Subscript[\[GothicCapitalA], j]
((Subscript[b, 1] + l)/Subscript[\[GothicCapitalB], 1]) >= 0) &&
1 <= j <= \[ScriptCapitalA] &&
!(Element[Subscript[d, j] - Subscript[\[GothicCapitalD], j]
((Subscript[b, 1] + l)/Subscript[\[GothicCapitalB], 1]), Integers] &&
Subscript[d, j] - Subscript[\[GothicCapitalD], j] ((Subscript[b, 1] + l)/
Subscript[\[GothicCapitalB], 1]) >= 0) &&
1 <= j <= \[ScriptCapitalD] &&
!(Element[-Subscript[c, j] - Subscript[\[GothicCapitalC], j]
((Subscript[b, 1] + l)/Subscript[\[GothicCapitalB], 1]), Integers] &&
-Subscript[c, j] - Subscript[\[GothicCapitalC], j]
((Subscript[b, 1] + l)/Subscript[\[GothicCapitalB], 1]) >= 0) &&
1 <= j <= \[ScriptCapitalC]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Residue", "[", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[ScriptCapitalA]"], RowBox[List["Gamma", "[", RowBox[List[RowBox[List[SubscriptBox["\[GothicCapitalA]", "k"], "s"]], "+", SubscriptBox["a", "k"]]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[ScriptCapitalB]"], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["b", "k"], "-", RowBox[List[SubscriptBox["\[GothicCapitalB]", "k"], "s"]]]], "]"]]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[ScriptCapitalC]"], RowBox[List["Gamma", "[", RowBox[List[RowBox[List[SubscriptBox["\[GothicCapitalC]", "k"], "s"]], "+", SubscriptBox["c", "k"]]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[ScriptCapitalD]"], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["d", "k"], "-", RowBox[List[SubscriptBox["\[GothicCapitalD]", "k"], "s"]]]], "]"]]]]]]], SuperscriptBox["z", RowBox[List["-", "s"]]]]], ",", RowBox[List["{", RowBox[List["s", ",", FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]], "}"]]]], "]"]], " ", "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["l", "-", "1"]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[ScriptCapitalA]"], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "k"], "+", RowBox[List[SubscriptBox["\[GothicCapitalA]", "k"], FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]]]], "]"]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "2"]], "\[ScriptCapitalB]"], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["b", "k"], "-", RowBox[List[SubscriptBox["\[GothicCapitalB]", "k"], FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]]]], "]"]]]]]]]]]], RowBox[List[SubscriptBox["\[GothicCapitalB]", "1"], RowBox[List["l", "!"]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[ScriptCapitalC]"], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["c", "k"], "+", RowBox[List[SubscriptBox["\[GothicCapitalC]", "k"], FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]]]], "]"]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[ScriptCapitalD]"], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["d", "k"], "-", RowBox[List[SubscriptBox["\[GothicCapitalD]", "k"], FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]]]], "]"]]]]]]]]]]], SuperscriptBox["z", RowBox[List["-", FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]]]]]]], "/;", RowBox[List[RowBox[List["l", "\[Element]", "Integers"]], "\[And]", RowBox[List["l", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["Not", "[", RowBox[List[RowBox[List[SubscriptBox["b", "j"], "-", RowBox[List[SubscriptBox["\[GothicCapitalB]", "j"], FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]]]], "\[Element]", "Integers"]], "]"]], "\[And]", RowBox[List["2", "\[LessEqual]", "j", "\[LessEqual]", "\[ScriptCapitalB]"]], "\[And]", RowBox[List["Not", "[", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", SubscriptBox["a", "j"]]], "-", RowBox[List[SubscriptBox["\[GothicCapitalA]", "j"], FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]]]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List[RowBox[List["-", SubscriptBox["a", "j"]]], "-", RowBox[List[SubscriptBox["\[GothicCapitalA]", "j"], FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]]]], "\[GreaterEqual]", "0"]]]], "]"]], "\[And]", RowBox[List["1", "\[LessEqual]", "j", "\[LessEqual]", "\[ScriptCapitalA]"]], "\[And]", RowBox[List["Not", "[", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["d", "j"], "-", RowBox[List[SubscriptBox["\[GothicCapitalD]", "j"], FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]]]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List[SubscriptBox["d", "j"], "-", RowBox[List[SubscriptBox["\[GothicCapitalD]", "j"], FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]]]], "\[GreaterEqual]", "0"]]]], "]"]], "\[And]", RowBox[List["1", "\[LessEqual]", "j", "\[LessEqual]", "\[ScriptCapitalD]"]], "\[And]", RowBox[List["Not", "[", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", SubscriptBox["c", "j"]]], "-", RowBox[List[SubscriptBox["\[GothicCapitalC]", "j"], FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]]]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List[RowBox[List["-", SubscriptBox["c", "j"]]], "-", RowBox[List[SubscriptBox["\[GothicCapitalC]", "j"], FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "l"]], SubscriptBox["\[GothicCapitalB]", "1"]]]]]], "\[GreaterEqual]", "0"]]]], "]"]], "\[And]", RowBox[List["1", "\[LessEqual]", "j", "\[LessEqual]", "\[ScriptCapitalC]"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <msub> <mi> res </mi> <mi> s </mi> </msub> <mo> ( </mo> <mrow> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> 𝒜 </mi> </munderover> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mrow> <mi> s </mi> <mo> ⁢ </mo> <msub> <mi> 𝔄 </mi> <mi> k </mi> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ℬ </mi> </munderover> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mi> k </mi> </msub> <mo> - </mo> <mrow> <msub> <mi> 𝔅 </mi> <mi> k </mi> </msub> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> 𝒞 </mi> </munderover> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> c </mi> <mi> k </mi> </msub> <mo> + </mo> <mrow> <mi> s </mi> <mo> ⁢ </mo> <msub> <mi> ℭ </mi> <mi> k </mi> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> 𝒟 </mi> </munderover> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> d </mi> <mi> k </mi> </msub> <mo> - </mo> <mrow> <msub> <mi> 𝔇 </mi> <mi> k </mi> </msub> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mfrac> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mi> l </mi> </mrow> <msub> <mi> 𝔅 </mi> <mn> 1 </mn> </msub> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> l </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> 𝒜 </mi> </munderover> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mrow> <msub> <mi> 𝔄 </mi> <mi> k </mi> </msub> <mo> ⁢ </mo> <mfrac> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mi> l </mi> </mrow> <msub> <mi> 𝔅 </mi> <mn> 1 </mn> </msub> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mi> ℬ </mi> </munderover> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mi> k </mi> </msub> <mo> - </mo> <mrow> <msub> <mi> 𝔅 </mi> <mi> k </mi> </msub> <mo> ⁢ </mo> <mfrac> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mi> l </mi> </mrow> <msub> <mi> 𝔅 </mi> <mn> 1 </mn> </msub> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mrow> <msub> <mi> 𝔅 </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mrow> <mi> l </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> 𝒞 </mi> </munderover> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> c </mi> <mi> k </mi> </msub> <mo> + </mo> <mrow> <msub> <mi> ℭ </mi> <mi> k </mi> </msub> <mo> ⁢ </mo> <mfrac> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mi> l </mi> </mrow> <msub> <mi> 𝔅 </mi> <mn> 1 </mn> </msub> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> 𝒟 </mi> </munderover> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> d </mi> <mi> k </mi> </msub> <mo> - </mo> <mrow> <msub> <mi> 𝔇 </mi> <mi> k </mi> </msub> <mo> ⁢ </mo> <mfrac> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mi> l </mi> </mrow> <msub> <mi> 𝔅 </mi> <mn> 1 </mn> </msub> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> l </mi> <mo> + </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <msub> <mi> 𝔅 </mi> <mn> 1 </mn> </msub> </mfrac> </mrow> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> l </mi> <mo> ∈ </mo> <semantics> <mi> ℕ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalN]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mrow> <msub> <mi> b </mi> <mi> j </mi> </msub> <mo> - </mo> <mrow> <msub> <mi> 𝔅 </mi> <mi> j </mi> </msub> <mo> ⁢ </mo> <mfrac> <mrow> <mtext> </mtext> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mi> l </mi> </mrow> </mrow> <msub> <mi> 𝔅 </mi> <mn> 1 </mn> </msub> </mfrac> </mrow> </mrow> <mo> ∉ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mn> 2 </mn> <mo> ≤ </mo> <mi> j </mi> <mo> ≤ </mo> <mi> ℬ </mi> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> - </mo> <mrow> <msub> <mi> 𝔄 </mi> <mi> j </mi> </msub> <mo> ⁢ </mo> <mfrac> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mi> l </mi> </mrow> <msub> <mi> 𝔅 </mi> <mn> 1 </mn> </msub> </mfrac> </mrow> </mrow> <mo> ∉ </mo> <semantics> <mi> ℕ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalN]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> j </mi> <mo> ≤ </mo> <mi> 𝒜 </mi> </mrow> <mo> ∧ </mo> <mrow> <mrow> <msub> <mi> d </mi> <mi> j </mi> </msub> <mo> - </mo> <mrow> <msub> <mi> 𝔇 </mi> <mi> j </mi> </msub> <mo> ⁢ </mo> <mfrac> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mi> l </mi> </mrow> <msub> <mi> 𝔅 </mi> <mn> 1 </mn> </msub> </mfrac> </mrow> </mrow> <mo> ∉ </mo> <semantics> <mi> ℕ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalN]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> j </mi> <mo> ≤ </mo> <mi> 𝒟 </mi> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> c </mi> <mi> j </mi> </msub> </mrow> <mo> - </mo> <mrow> <msub> <mi> ℭ </mi> <mi> j </mi> </msub> <mo> ⁢ </mo> <mfrac> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mi> l </mi> </mrow> <msub> <mi> 𝔅 </mi> <mn> 1 </mn> </msub> </mfrac> </mrow> </mrow> <mo> ∉ </mo> <semantics> <mi> ℕ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalN]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> j </mi> <mo> ≤ </mo> <mi> 𝒞 </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> res </ci> <ci> s </ci> </apply> <apply> <times /> <apply> <times /> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> 𝒜 </ci> </uplimit> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <ci> s </ci> <apply> <ci> Subscript </ci> <ci> 𝔄 </ci> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> ℬ </ci> </uplimit> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> 𝔅 </ci> <ci> k </ci> </apply> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> 𝒞 </ci> </uplimit> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <ci> s </ci> <apply> <ci> Subscript </ci> <ci> ℭ </ci> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> 𝒟 </ci> </uplimit> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> d </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> 𝔇 </ci> <ci> k </ci> </apply> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> l </ci> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> 𝔅 </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> l </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> 𝒜 </ci> </uplimit> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> 𝔄 </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> l </ci> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> 𝔅 </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <ci> ℬ </ci> </uplimit> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> 𝔅 </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> l </ci> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> 𝔅 </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> 𝔅 </ci> <cn type='integer'> 1 </cn> </apply> <apply> <factorial /> <ci> l </ci> </apply> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> 𝒞 </ci> </uplimit> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> ℭ </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> l </ci> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> 𝔅 </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> 𝒟 </ci> </uplimit> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> d </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> 𝔇 </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> l </ci> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> 𝔅 </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> l </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> 𝔅 </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> l </ci> <integers /> </apply> 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type='integer'> 1 </cn> </apply> <ci> l </ci> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> 𝔅 </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <integers /> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> j </ci> <ci> 𝒜 </ci> </apply> <apply> <notin /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> d </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> 𝔇 </ci> <ci> j </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> l </ci> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> 𝔅 </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <integers /> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> j </ci> <ci> 𝒟 </ci> </apply> <apply> <notin /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> c </ci> <ci> j </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> ℭ </ci> <ci> j </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> l </ci> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> 𝔅 </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <integers /> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> j </ci> <ci> 𝒞 </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
