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http://functions.wolfram.com/07.28.13.0016.01
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(1 - z) z^3 Derivative[4][w][z] + (3 + Subscript[b, 1] + Subscript[b, 2] +
Subscript[b, 3] - (6 + Subscript[a, 1] + Subscript[a, 2] +
Subscript[a, 3] + Subscript[a, 4]) z) z^2 Derivative[3][w][z] +
(1 + Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3] +
Subscript[b, 1] Subscript[b, 2] + Subscript[b, 2] Subscript[b, 3] +
Subscript[b, 1] Subscript[b, 3] - (7 + 3 Subscript[a, 1] +
3 Subscript[a, 2] + 3 Subscript[a, 3] + 3 Subscript[a, 4] +
Subscript[a, 1] Subscript[a, 2] + Subscript[a, 1] Subscript[a, 3] +
Subscript[a, 1] Subscript[a, 4] + Subscript[a, 2] Subscript[a, 3] +
Subscript[a, 2] Subscript[a, 4] + Subscript[a, 3] Subscript[a, 4]) z)
z Derivative[2][w][z] +
(Subscript[b, 1] Subscript[b, 2] Subscript[b, 3] -
(1 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 1]
Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] +
Subscript[a, 1] Subscript[a, 3] + Subscript[a, 2] Subscript[a, 3] +
Subscript[a, 1] Subscript[a, 4] + Subscript[a, 2] Subscript[a, 4] +
Subscript[a, 3] Subscript[a, 4] + Subscript[a, 1] Subscript[a, 2]
Subscript[a, 3] + Subscript[a, 1] Subscript[a, 2] Subscript[a, 4] +
Subscript[a, 1] Subscript[a, 3] Subscript[a, 4] +
Subscript[a, 2] Subscript[a, 3] Subscript[a, 4]) z)
Derivative[1][w][z] - Subscript[a, 1] Subscript[a, 2] Subscript[a, 3]
Subscript[a, 4] w[z] == 0 /;
w[z] == (Subscript[c, 1] HypergeometricPFQRegularized[
{Subscript[a, 1], 1 + Subscript[a, 1] - Subscript[b, 1],
1 + Subscript[a, 1] - Subscript[b, 2], 1 + Subscript[a, 1] -
Subscript[b, 3]}, {1 + Subscript[a, 1] - Subscript[a, 2],
1 + Subscript[a, 1] - Subscript[a, 3], 1 + Subscript[a, 1] -
Subscript[a, 4]}, 1/z])/z^Subscript[a, 1] +
(Subscript[c, 2] HypergeometricPFQRegularized[{Subscript[a, 2],
1 + Subscript[a, 2] - Subscript[b, 1], 1 + Subscript[a, 2] -
Subscript[b, 2], 1 + Subscript[a, 2] - Subscript[b, 3]},
{1 + Subscript[a, 2] - Subscript[a, 1], 1 + Subscript[a, 2] -
Subscript[a, 3], 1 + Subscript[a, 2] - Subscript[a, 4]}, 1/z])/
z^Subscript[a, 2] + (Subscript[c, 3] HypergeometricPFQRegularized[
{Subscript[a, 3], 1 + Subscript[a, 3] - Subscript[b, 1],
1 + Subscript[a, 3] - Subscript[b, 2], 1 + Subscript[a, 3] -
Subscript[b, 3]}, {1 + Subscript[a, 3] - Subscript[a, 1],
1 + Subscript[a, 3] - Subscript[a, 2], 1 + Subscript[a, 3] -
Subscript[a, 4]}, 1/z])/z^Subscript[a, 3] +
(Subscript[c, 4] HypergeometricPFQRegularized[{Subscript[a, 4],
1 + Subscript[a, 4] - Subscript[b, 1], 1 + Subscript[a, 4] -
Subscript[b, 2], 1 + Subscript[a, 4] - Subscript[b, 3]},
{1 + Subscript[a, 4] - Subscript[a, 1], 1 + Subscript[a, 4] -
Subscript[a, 2], 1 + Subscript[a, 4] - Subscript[a, 3]}, 1/z])/
z^Subscript[a, 4] && !Element[Subscript[a, 1] - Subscript[a, 2],
Integers] && !Element[Subscript[a, 1] - Subscript[a, 3], Integers] &&
!Element[Subscript[a, 1] - Subscript[a, 4], Integers] &&
!Element[Subscript[a, 2] - Subscript[a, 3], Integers] &&
!Element[Subscript[a, 2] - Subscript[a, 4], Integers] &&
!Element[Subscript[a, 3] - Subscript[a, 4], Integers]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], " ", SuperscriptBox["z", "3"], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "4", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["3", "+", SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"], "+", SubscriptBox["b", "3"], "-", RowBox[List[RowBox[List["(", RowBox[List["6", "+", SubscriptBox["a", "1"], "+", SubscriptBox["a", "2"], "+", SubscriptBox["a", "3"], "+", SubscriptBox["a", "4"]]], ")"]], " ", "z"]]]], ")"]], " ", SuperscriptBox["z", "2"], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"], "+", SubscriptBox["b", "3"], "+", RowBox[List[SubscriptBox["b", "1"], " ", SubscriptBox["b", "2"]]], "+", 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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> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <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> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <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> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 4 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <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> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <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> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 4 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> a </mi> <mn> 4 </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> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> <mo> 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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,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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