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http://functions.wolfram.com/07.31.06.0041.01
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HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, p]},
{Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] \[Proportional]
Sum[(Subscript[c, k] (1 + O[1/z]))/(-z)^Subscript[a, k], {k, 1, p}] +
KroneckerDelta[q, p + 1] Subscript[e, 1] (-z)^\[Chi]
Cos[2 Sqrt[-z] + \[Chi] Pi] (1 + O[1/Sqrt[-z]]) +
(UnitStep[q - p] - KroneckerDelta[q, p + 1]) Subscript[e, 2] z^\[Chi]
Exp[\[Beta] z^(1/\[Beta])] (1 + O[1/z^(1/\[Beta])]) /;
(Abs[z] -> Infinity) && \[Beta] == q - p + 1 &&
\[Chi] == (1/\[Beta]) ((\[Beta] - 1)/2 + Sum[Subscript[a, k], {k, 1, p}] -
Sum[Subscript[b, k], {k, 1, q}]) && Subscript[c, k] ==
(Gamma[Subscript[a, k]] Product[Gamma[Subscript[b, j]], {j, 1, q}]
Product[If[j == k, 1, Gamma[Subscript[a, j] - Subscript[a, k]]],
{j, 1, p}])/(Product[Gamma[Subscript[a, j]], {j, 1, p}]
Product[Gamma[Subscript[b, j] - Subscript[a, k]], {j, 1, q}]) &&
2 Subscript[e, 2] == Subscript[e, 1] ==
((2 (2 Pi)^((1 - \[Beta])/2))/Sqrt[\[Beta]])
(Product[Gamma[Subscript[b, k]], {k, 1, q}]/
Product[Gamma[Subscript[a, k]], {k, 1, p}]) &&
ForAll[{j, k}, Element[{j, k}, Integers] && j != k && 1 <= j <= p &&
1 <= k <= p, Subscript[a, j] != Subscript[a, k]]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "p"], RowBox[List[SubscriptBox["c", "k"], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", SubscriptBox["a", "k"]]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", "z"], "]"]]]], ")"]]]]]], "+", RowBox[List[RowBox[List["KroneckerDelta", "[", RowBox[List["q", ",", RowBox[List["p", "+", "1"]]]], "]"]], SubscriptBox["e", "1"], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], "\[Chi]"], RowBox[List["Cos", "[", RowBox[List[RowBox[List["2", " ", SqrtBox[RowBox[List["-", "z"]]]]], "+", RowBox[List["\[Chi]", " ", "\[Pi]"]]]], "]"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", SqrtBox[RowBox[List["-", "z"]]]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["q", "-", "p"]], "]"]], "-", RowBox[List["KroneckerDelta", "[", RowBox[List["q", ",", RowBox[List["p", "+", "1"]]]], "]"]]]], ")"]], SubscriptBox["e", "2"], " ", SuperscriptBox["z", "\[Chi]"], " ", RowBox[List["Exp", "[", RowBox[List["\[Beta]", " ", SuperscriptBox["z", FractionBox["1", "\[Beta]"]]]], "]"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", RowBox[List["1", "/", "\[Beta]"]]]], "]"]]]], ")"]]]]]]]], "/;", "\[InvisibleSpace]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "\[And]", RowBox[List["\[Beta]", "\[Equal]", RowBox[List["q", "-", "p", "+", "1"]]]], "\[And]", RowBox[List["\[Chi]", "\[Equal]", RowBox[List[FractionBox["1", "\[Beta]"], RowBox[List["(", RowBox[List[FractionBox[RowBox[List["\[Beta]", "-", "1"]], "2"], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "p"], SubscriptBox["a", "k"]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "q"], SubscriptBox["b", "k"]]]]], ")"]]]]]], "\[And]", RowBox[List[SubscriptBox["c", "k"], "\[Equal]", FractionBox[RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["a", "k"], "]"]], RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["Gamma", "[", SubscriptBox["b", "j"], "]"]]]], ")"]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["If", "[", RowBox[List[RowBox[List["j", "\[Equal]", "k"]], ",", "1", ",", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "j"], "-", SubscriptBox["a", "k"]]], "]"]]]], "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["Gamma", "[", SubscriptBox["a", "j"], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["b", "j"], "-", SubscriptBox["a", "k"]]], "]"]]]]]]]]], "\[And]", RowBox[List[RowBox[List["2", SubscriptBox["e", "2"]]], "\[Equal]", SubscriptBox["e", "1"], "\[Equal]", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]], FractionBox[RowBox[List["1", "-", "\[Beta]"]], "2"]], " "]], SqrtBox["\[Beta]"]], FractionBox[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "q"], RowBox[List["Gamma", "[", SubscriptBox["b", "k"], "]"]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "p"], RowBox[List["Gamma", "[", SubscriptBox["a", "k"], "]"]]]]]]]]], "\[And]", RowBox[List[SubscriptBox["\[ForAll]", RowBox[List[RowBox[List["{", RowBox[List["j", ",", "k"]], "}"]], ",", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["j", ",", "k"]], "}"]], "\[Element]", "Integers"]], "\[And]", RowBox[List["j", "\[NotEqual]", "k"]], "\[And]", RowBox[List["1", "\[LessEqual]", "j", "\[LessEqual]", "p"]], "\[And]", RowBox[List["1", "\[LessEqual]", "k", "\[LessEqual]", "p"]]]]]]], RowBox[List["(", RowBox[List[SubscriptBox["a", "j"], "\[NotEqual]", SubscriptBox["a", "k"]]], ")"]]]]]]]]]]
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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> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mi> p </mi> </msub> <msub> <mi> F </mi> <mi> q </mi> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> <mo> ; </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] </annotation> </semantics> <mo> ∝ </mo> <mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <msub> <mi> c </mi> <mi> k </mi> </msub> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> + </mo> <mtext> </mtext> <mrow> <msub> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <mi> q </mi> <mo> , </mo> <mrow> <mi> p </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> </msub> <mo> ⁢ </mo> <msub> <mi> e </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mi> χ </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> χ </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mfrac> <mn> 1 </mn> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mi> θ </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <msub> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <mi> q </mi> <mo> , </mo> <mrow> <mi> p </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> e </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> χ </mi> </msup> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> β </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 1 </mn> <mo> / </mo> <mi> β </mi> </mrow> </msup> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mrow> <mn> 1 </mn> <mo> / </mo> <mi> β </mi> </mrow> </msup> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∧ </mo> <mrow> <mi> β </mi> <mo> ⩵ </mo> <mrow> <mi> q </mi> <mo> - </mo> <mi> p </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mi> χ </mi> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> β </mi> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> β </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> + </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <msub> <mi> a </mi> <mi> k </mi> </msub> </mrow> <mo> - </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <msub> <mi> b </mi> <mi> k </mi> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> c </mi> <mi> k </mi> </msub> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <munder> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> j </mi> <mo> ≠ </mo> <mi> k </mi> </mrow> </munder> <mi> p </mi> </munderover> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> e </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⩵ </mo> <msub> <mi> e </mi> <mn> 1 </mn> </msub> <mo> ⩵ </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> β </mi> </mrow> <mn> 2 </mn> </mfrac> </msup> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> b </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <msqrt> <mi> β </mi> </msqrt> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo> ∧ </mo> <mrow> <msub> <mo> ∀ </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mi> j </mi> <mo> , </mo> <mi> k </mi> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mrow> <mrow> <mo> { </mo> <mrow> <mi> j </mi> <mo> , </mo> <mi> k </mi> </mrow> <mo> } </mo> </mrow> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> j </mi> <mo> ≠ </mo> <mi> k </mi> </mrow> <mo> ∧ </mo> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> j </mi> <mo> ≤ </mo> <mi> p </mi> </mrow> <mo> ∧ </mo> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> k </mi> <mo> ≤ </mo> <mi> p </mi> </mrow> </mrow> </mrow> </msub> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> ≠ </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> TagBox </ci> <apply> <ci> TagBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms>  </ms> <apply> <ci> FormBox </ci> <ms> p </ms> <ci> TraditionalForm </ci> </apply> </apply> <apply> <ci> SubscriptBox </ci> <ms> F </ms> <apply> <ci> FormBox </ci> <ms> q </ms> <ci> TraditionalForm </ci> </apply> </apply> </list> </apply> <ms> ⁡ </ms> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> TagBox </ci> <apply> <ci> TagBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> TagBox </ci> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> 1 </ms> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <ms> , </ms> <apply> <ci> TagBox </ci> <ms> … </ms> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <ms> , </ms> <apply> <ci> TagBox </ci> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> p </ms> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> </list> </apply> <apply> <ci> InterpretTemplate </ci> <apply> <ci> Function </ci> <list> <apply> <ci> SlotSequence </ci> <cn type='integer'> 1 </cn> </apply> </list> </apply> </apply> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <ms> ; </ms> <apply> <ci> TagBox </ci> <apply> <ci> TagBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> TagBox </ci> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> 1 </ms> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <ms> , </ms> <apply> <ci> TagBox </ci> <ms> … </ms> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <ms> , </ms> <apply> <ci> TagBox </ci> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> q </ms> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> </list> </apply> <apply> <ci> InterpretTemplate </ci> <apply> <ci> Function </ci> <list> <apply> <ci> SlotSequence </ci> <cn type='integer'> 1 </cn> </apply> </list> </apply> </apply> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <ms> ; </ms> <apply> <ci> TagBox </ci> <ms> z </ms> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <apply> <ci> InterpretTemplate </ci> <apply> <ci> Function </ci> <apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Slot </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Slot </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Slot </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <ci> HypergeometricPFQ </ci> </apply> <ms> ∝ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> ∑ </ms> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> p </ms> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> c </ms> <ms> k </ms> </apply> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> z </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> k </ms> </apply> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <ms> O </ms> <ms> ( </ms> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <ms> z </ms> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <apply> <ci> InterpretationBox </ci> <ms> δ </ms> <ci> KroneckerDelta </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <false /> </apply> <apply> <ci> Rule </ci> <ci> Selectable </ci> <false /> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> q </ms> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <ms> p </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> </list> </apply> </apply> <apply> <ci> SubscriptBox </ci> <ms> e </ms> <ms> 1 </ms> </apply> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> z </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> χ </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> cos </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> π </ms> <ms> χ </ms> </list> </apply> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <apply> <ci> SqrtBox </ci> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> z </ms> </list> </apply> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <ms> O </ms> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <apply> <ci> SqrtBox </ci> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> z </ms> </list> </apply> </apply> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> InterpretationBox </ci> <ms> θ </ms> <ci> UnitStep </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <false /> </apply> <apply> <ci> Rule </ci> <ci> Selectable </ci> <false /> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> q </ms> <ms> - </ms> <ms> p </ms> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <apply> <ci> InterpretationBox </ci> <ms> δ </ms> <ci> KroneckerDelta </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <false /> </apply> <apply> <ci> Rule </ci> <ci> Selectable </ci> <false /> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> q </ms> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <ms> p </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> </list> </apply> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> SubscriptBox </ci> <ms> e </ms> <ms> 2 </ms> </apply> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <ms> χ </ms> </apply> <apply> <ci> SuperscriptBox </ci> <ms> ⅇ </ms> <apply> <ci> RowBox </ci> <list> <ms> β </ms> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> / </ms> <ms> β </ms> </list> </apply> </apply> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <ms> O </ms> <ms> ( </ms> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> / </ms> <ms> β </ms> </list> </apply> </apply> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms>  </ms> <ms> z </ms> <ms>  </ms> </list> </apply> <ms>  </ms> <ms> ∞ </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> ∧ </ms> <apply> <ci> RowBox </ci> <list> <ms> β </ms> <ms> ⩵ </ms> <apply> <ci> RowBox </ci> <list> <ms> q </ms> <ms> - </ms> <ms> p </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> </list> </apply> <ms> ∧ </ms> <apply> <ci> RowBox </ci> <list> <ms> χ </ms> <ms> ⩵ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <ms> β </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> β </ms> <ms> - </ms> <ms> 1 </ms> </list> </apply> <ms> 2 </ms> </apply> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> ∑ </ms> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> p </ms> </apply> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> k </ms> </apply> </list> </apply> <ms> - </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> ∑ </ms> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> q </ms> </apply> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> k </ms> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> <ms> ∧ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> c </ms> <ms> k </ms> </apply> <ms> ⩵ </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> k </ms> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> ∏ </ms> <apply> <ci> RowBox </ci> <list> <ms> j </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> q </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> j </ms> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> ErrorBox </ci> <apply> <ci> UnderoverscriptBox </ci> <ms> ∏ </ms> <apply> <ci> UnderscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> j </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> j </ms> <ms> ≠ </ms> <ms> k </ms> </list> </apply> </apply> <ms> p </ms> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> j </ms> </apply> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> k </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> ∏ </ms> <apply> <ci> RowBox </ci> <list> <ms> j </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> p </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> j </ms> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> ∏ </ms> <apply> <ci> RowBox </ci> <list> <ms> j </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> q </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> j </ms> </apply> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> k </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> </apply> </list> </apply> <ms> ∧ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <apply> <ci> SubscriptBox </ci> <ms> e </ms> <ms> 2 </ms> </apply> </list> </apply> <ms> ⩵ </ms> <apply> <ci> SubscriptBox </ci> <ms> e </ms> <ms> 1 </ms> </apply> <ms> ⩵ </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> π </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> β </ms> </list> </apply> <ms> 2 </ms> </apply> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> ∏ </ms> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> q </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> k </ms> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SqrtBox </ci> <ms> β </ms> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> ∏ </ms> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> p </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> k </ms> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> </apply> </list> </apply> <ms> ∧ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> ∀ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> { </ms> <apply> <ci> RowBox </ci> <list> <ms> j </ms> <ms> , </ms> <ms> k </ms> </list> </apply> <ms> } </ms> </list> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> { </ms> <apply> <ci> RowBox </ci> <list> <ms> j </ms> <ms> , </ms> <ms> k </ms> </list> </apply> <ms> } </ms> </list> </apply> <ms> ∈ </ms> <apply> <ci> TagBox </ci> <ms> ℤ </ms> <apply> <ci> Function </ci> <integers /> </apply> </apply> </list> </apply> <ms> ∧ </ms> <apply> <ci> RowBox </ci> <list> <ms> j </ms> <ms> ≠ </ms> <ms> k </ms> </list> </apply> <ms> ∧ </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> ≤ </ms> <ms> j </ms> <ms> ≤ </ms> <ms> p </ms> </list> </apply> <ms> ∧ </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> ≤ </ms> <ms> k </ms> <ms> ≤ </ms> <ms> p </ms> </list> </apply> </list> </apply> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> j </ms> </apply> <ms> ≠ </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> k </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1},z] | HypergeometricPFQ[{a1,a2},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] | |
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