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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.13.0006.01

 Input Form

 Wronskian[HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z], z^(1 - Subscript[b, 1]) HypergeometricPFQ[ {1 + Subscript[a, 1] - Subscript[b, 1], 1 + Subscript[a, 2] - Subscript[b, 1], 1 + Subscript[a, 3] - Subscript[b, 1]}, {2 - Subscript[b, 1], 1 - Subscript[b, 1] + Subscript[b, 2]}, z], z^(1 - Subscript[b, 2]) HypergeometricPFQ[ {1 + Subscript[a, 1] - Subscript[b, 2], 1 + Subscript[a, 2] - Subscript[b, 2], 1 + Subscript[a, 3] - Subscript[b, 2]}, {2 - Subscript[b, 2], 1 + Subscript[b, 1] - Subscript[b, 2]}, z], z] == (-1 + Subscript[b, 1]) (-1 + Subscript[b, 2]) (Subscript[b, 1] - Subscript[b, 2]) (1 - z)^(-2 - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3] + Subscript[b, 1] + Subscript[b, 2]) z^(-1 - Subscript[b, 1] - Subscript[b, 2])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", SubscriptBox["a", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"]]], "}"]], ",", "z"]], "]"]], ",", RowBox[List[SuperscriptBox["z", RowBox[List["1", "-", SubscriptBox["b", "1"]]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "2"], "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "3"], "-", SubscriptBox["b", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"]]]]], "}"]], ",", "z"]], "]"]]]], ",", " ", RowBox[List[SuperscriptBox["z", RowBox[List["1", "-", SubscriptBox["b", "2"]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "2"], "-", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "3"], "-", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]]]], "}"]], ",", "z"]], "]"]]]], ",", " ", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SubscriptBox["b", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SubscriptBox["b", "2"]]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", SubscriptBox["a", "1"], "-", SubscriptBox["a", "2"], "-", SubscriptBox["a", "3"], "+", SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"]]]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "-", SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]]]]]]]]]

 MathML Form

 W z ( 3 F 2 ( a 1 , a 2 , a 3 ; b 1 , b 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] , z 1 - b 1 3 F 2 ( a 1 - b 1 + 1 , a 2 - b 1 + 1 , a 3 - b 1 + 1 ; 2 - b 1 , - b 1 + b 2 + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["b", "1"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["b", "1"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "3"], "-", SubscriptBox["b", "1"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["2", "-", SubscriptBox["b", "1"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", SubscriptBox["b", "1"]]], "+", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] , z 1 - b 2 3 F 2 ( a 1 - b 2 + 1 , a 2 - b 2 + 1 , a 3 - b 2 + 1 ; 2 - b 2 , b 1 - b 2 + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "3"], "-", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["2", "-", SubscriptBox["b", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) ( b 1 - 1 ) ( b 2 - 1 ) ( b 1 - b 2 ) ( 1 - z ) - a 1 - a 2 - a 3 + b 1 + b 2 - 2 z - b 1 - b 2 - 1 Subscript W z HypergeometricPFQ Subscript a 1 Subscript a 2 Subscript a 3 Subscript b 1 Subscript b 2 z z 1 -1 Subscript b 1 HypergeometricPFQ Subscript a 1 -1 Subscript b 1 1 Subscript a 2 -1 Subscript b 1 1 Subscript a 3 -1 Subscript b 1 1 2 -1 Subscript b 1 -1 Subscript b 1 Subscript b 2 1 z z 1 -1 Subscript b 2 HypergeometricPFQ Subscript a 1 -1 Subscript b 2 1 Subscript a 2 -1 Subscript b 2 1 Subscript a 3 -1 Subscript b 2 1 2 -1 Subscript b 2 Subscript b 1 -1 Subscript b 2 1 z Subscript b 1 -1 Subscript b 2 -1 Subscript b 1 -1 Subscript b 2 1 -1 z -1 Subscript a 1 -1 Subscript a 2 -1 Subscript a 3 Subscript b 1 Subscript b 2 -2 z -1 Subscript b 1 -1 Subscript b 2 -1 [/itex]

 Rule Form

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

 2007-05-02