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http://functions.wolfram.com/07.26.13.0002.01
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z^3 Derivative[4][w][z] + (Subscript[b, 1] + Subscript[b, 2] +
Subscript[b, 3] + 3) z^2 Derivative[3][w][z] +
(Subscript[b, 1] Subscript[b, 2] + Subscript[b, 2] Subscript[b, 3] +
Subscript[b, 1] Subscript[b, 3] + Subscript[b, 1] + Subscript[b, 2] +
Subscript[b, 3] + 1 - z) z Derivative[2][w][z] +
(Subscript[b, 1] Subscript[b, 2] Subscript[b, 3] -
(Subscript[a, 1] + Subscript[a, 2] + 1) z) Derivative[1][w][z] -
Subscript[a, 1] Subscript[a, 2] w[z] == 0 /;
w[z] == Subscript[c, 1] HypergeometricPFQRegularized[
{Subscript[a, 1], Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2],
Subscript[b, 3]}, z] + Subscript[c, 2]
(MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}},
{{0, 1 - Subscript[b, 1]}, {1 - Subscript[b, 2], 1 - Subscript[b, 3]}},
z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}},
{{0, 1 - Subscript[b, 2]}, {1 - Subscript[b, 1], 1 - Subscript[b, 3]}},
z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}},
{{0, 1 - Subscript[b, 3]}, {1 - Subscript[b, 1], 1 - Subscript[b, 2]}},
z]) + Subscript[c, 3]
(MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}},
{{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}, {1 - Subscript[b, 3]}},
-z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}},
{{0, 1 - Subscript[b, 1], 1 - Subscript[b, 3]}, {1 - Subscript[b, 2]}},
-z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}},
{{0, 1 - Subscript[b, 2], 1 - Subscript[b, 3]}, {1 - Subscript[b, 1]}},
-z]) + Subscript[c, 4] MeijerG[{{1 - Subscript[a, 1],
1 - Subscript[a, 2]}, {}}, {{0, 1 - Subscript[b, 1],
1 - Subscript[b, 2], 1 - Subscript[b, 3]}, {}}, z]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["z", "3"], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "4", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"], "+", SubscriptBox["b", "3"], "+", "3"]], ")"]], " ", SuperscriptBox["z", "2"], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["b", "1"], " ", SubscriptBox["b", "2"]]], "+", RowBox[List[SubscriptBox["b", "2"], " ", SubscriptBox["b", "3"]]], "+", RowBox[List[SubscriptBox["b", "1"], " ", SubscriptBox["b", "3"]]], "+", SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"], "+", SubscriptBox["b", "3"], "+", "1", "-", "z"]], ")"]], " ", "z", " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", 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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> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <mrow> <msup> <mi> w </mi> <semantics> <mrow> <mo> ( </mo> <mn> 4 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", "4", ")"]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <msup> <mi> w </mi> <semantics> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", "3", ")"]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mtext> </mtext> <mrow> <msup> <mi> w </mi> <mi> ′′ </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> w </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <msub> <mi> c </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 3 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> ; </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox[OverscriptBox["F", "~"], "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, 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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,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] | | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] | | |
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){kind=small}
