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 HypergeometricPFQ

 http://functions.wolfram.com/07.25.17.0003.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, {b, Subscript[b, 2]}, z] == (Subscript[B, 1] + Subscript[C, 1] z) HypergeometricPFQ[ {Subscript[a, 1], Subscript[a, 2]}, {b + 1, Subscript[b, 2]}, z] + (Subscript[B, 2] + Subscript[C, 2] z) HypergeometricPFQ[ {Subscript[a, 1], Subscript[a, 2]}, {b + 2, Subscript[b, 2]}, z] + Subscript[C, 3] z HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, {b + 3, Subscript[b, 2]}, z] /; Subscript[B, 1] == (2 + 2 b - Subscript[b, 2])/b && Subscript[C, 1] == 1/b && Subscript[B, 2] == (Subscript[b, 2] - b - 2)/b && Subscript[C, 2] == (Subscript[a, 1] + Subscript[a, 2] - 2 b - 3)/ (b (1 + b)) && Subscript[C, 3] == ((2 + b - Subscript[a, 1]) (2 + b - Subscript[a, 2]))/(b (1 + b) (2 + b))

 Standard Form

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 MathML Form

 2 F 2 ( a 1 , a 2 ; b , b 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[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]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["b", 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] ( B 1 + C 1 z ) 2 F 2 ( a 1 , a 2 ; b + 1 , b 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[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]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["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] + ( B 2 + C 2 z ) 2 F 2 ( a 1 , a 2 ; b + 2 , b 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[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]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["b", "+", "2"]], 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] + C 3 z 2 F 2 ( a 1 , a 2 ; b + 3 , b 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[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]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["b", "+", "3"]], 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] /; B 1 2 b - b 2 + 2 b C 1 1 b B 2 b 2 - b - 2 b C 2 a 1 + a 2 - 2 b - 3 b ( b + 1 ) C 3 ( b - a 1 + 2 ) ( b - a 2 + 2 ) b ( b + 1 ) ( b + 2 ) Condition HypergeometricPFQ Subscript a 1 Subscript a 2 b Subscript b 2 z Subscript B 1 Subscript C 1 z HypergeometricPFQ Subscript a 1 Subscript a 2 b 1 Subscript b 2 z Subscript B 2 Subscript C 2 z HypergeometricPFQ Subscript a 1 Subscript a 2 b 2 Subscript b 2 z Subscript C 3 z HypergeometricPFQ Subscript a 1 Subscript a 2 b 3 Subscript b 2 z Subscript B 1 2 b -1 Subscript b 2 2 b -1 Subscript C 1 1 b -1 Subscript B 2 Subscript b 2 -1 b -2 b -1 Subscript C 2 Subscript a 1 Subscript a 2 -1 2 b -3 b b 1 -1 Subscript C 3 b -1 Subscript a 1 2 b -1 Subscript a 2 2 b b 1 b 2 -1 [/itex]

 Rule Form

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

 2001-10-29