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 HypergeometricPFQ

 http://functions.wolfram.com/07.26.20.0027.02

 Input Form

 D[z^\[Alpha] HypergeometricPFQ[{-(n/2), (-n + 1)/2}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z^m], {z, n}] == (-1)^n Pochhammer[-\[Alpha], n] z^(\[Alpha] - n) HypergeometricPFQ[{-(n/2), (-n + 1)/2, (\[Alpha] + 1)/m, (\[Alpha] + 2)/m, \[Ellipsis], (\[Alpha] + m)/m}, {(\[Alpha] - n + 1)/m, (\[Alpha] - n + 2)/m, \[Ellipsis], (\[Alpha] - n + m)/m, Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z^m] /; Element[m, Integers] && m > 0 && Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "n"]], "}"]]], RowBox[List["(", RowBox[List[SuperscriptBox["z", "\[Alpha]"], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], ",", FractionBox[RowBox[List[RowBox[List["-", "n"]], "+", "1"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"], ",", SubscriptBox["b", "3"]]], "}"]], ",", SuperscriptBox["z", "m"]]], "]"]]]], ")"]]]], "\[Equal]", " ", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "\[Alpha]"]], ",", "n"]], "]"]], SuperscriptBox["z", RowBox[List["\[Alpha]", "-", "n"]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], ",", FractionBox[RowBox[List[RowBox[List["-", "n"]], "+", "1"]], "2"], ",", FractionBox[RowBox[List["\[Alpha]", "+", "1"]], "m"], ",", FractionBox[RowBox[List["\[Alpha]", "+", "2"]], "m"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["\[Alpha]", "+", "m"]], "m"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["\[Alpha]", "-", "n", "+", "1"]], "m"], ",", FractionBox[RowBox[List["\[Alpha]", "-", "n", "+", "2"]], "m"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["\[Alpha]", "-", "n", "+", "m"]], "m"], ",", SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"], ",", SubscriptBox["b", "3"]]], "}"]], ",", SuperscriptBox["z", "m"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 n ( z α 2 F 3 ( - n 2 , 1 - n 2 ; b 1 , b 2 , b 3 ; z m ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["n", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["1", "-", "n"]], "2"], 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]], ",", TagBox[SubscriptBox["b", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[SuperscriptBox["z", "m"], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) z n ( - 1 ) n ( - α ) n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", "\[Alpha]"]], ")"]], "n"], Pochhammer] z α - n m + 2 F m + 3 ( - n 2 TagBox[RowBox[List["-", FractionBox["n", "2"]]], HypergeometricPFQ, Rule[Editable, True]] , 1 - n 2 TagBox[FractionBox[RowBox[List["1", "-", "n"]], "2"], HypergeometricPFQ, Rule[Editable, True]] , α + 1 m TagBox[FractionBox[RowBox[List["\[Alpha]", "+", "1"]], "m"], HypergeometricPFQ, Rule[Editable, True]] , α + 2 m TagBox[FractionBox[RowBox[List["\[Alpha]", "+", "2"]], "m"], HypergeometricPFQ, Rule[Editable, True]] , TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]] , α + m m TagBox[FractionBox[RowBox[List["\[Alpha]", "+", "m"]], "m"], HypergeometricPFQ, Rule[Editable, True]] ; α - n + 1 m , α - n + 2 m , , α - n + m m , b 1 TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]] , b 2 TagBox[SubscriptBox["b", "2"], HypergeometricPFQ, Rule[Editable, True]] , b 3 TagBox[SubscriptBox["b", "3"], HypergeometricPFQ, Rule[Editable, True]] ; z m TagBox[SuperscriptBox["z", "m"], HypergeometricPFQ, Rule[Editable, True]] ) /; m + n FormBox RowBox RowBox FractionBox RowBox SuperscriptBox n RowBox ( RowBox SuperscriptBox z α TagBox TagBox RowBox RowBox SubscriptBox FormBox 2 TraditionalForm SubscriptBox F FormBox 3 TraditionalForm RowBox ( RowBox TagBox TagBox RowBox TagBox RowBox - FractionBox n 2 HypergeometricPFQ Rule Editable , TagBox FractionBox RowBox 1 - n 2 HypergeometricPFQ Rule Editable InterpretTemplate Function SlotSequence 1 HypergeometricPFQ Rule Editable ; TagBox TagBox RowBox TagBox SubscriptBox b 1 HypergeometricPFQ Rule Editable , TagBox SubscriptBox b 2 HypergeometricPFQ Rule Editable , TagBox SubscriptBox b 3 HypergeometricPFQ Rule Editable InterpretTemplate Function SlotSequence 1 HypergeometricPFQ Rule Editable ; TagBox SuperscriptBox z m HypergeometricPFQ Rule Editable ) InterpretTemplate Function HypergeometricPFQ Slot 1 Slot 2 Slot 3 Rule Editable HypergeometricPFQ ) RowBox SuperscriptBox z n RowBox SuperscriptBox RowBox ( RowBox - 1 ) n TagBox SubscriptBox RowBox ( RowBox - α ) n Pochhammer SuperscriptBox z RowBox α - n RowBox RowBox SubscriptBox ErrorBox RowBox m + 2 SubscriptBox F FormBox RowBox m + 3 TraditionalForm RowBox ( RowBox TagBox RowBox - FractionBox n 2 HypergeometricPFQ Rule Editable , TagBox FractionBox RowBox 1 - n 2 HypergeometricPFQ Rule Editable , TagBox FractionBox RowBox α + 1 m HypergeometricPFQ Rule Editable , TagBox FractionBox RowBox α + 2 m HypergeometricPFQ Rule Editable , TagBox HypergeometricPFQ Rule Editable , RowBox TagBox FractionBox RowBox α + m m HypergeometricPFQ Rule Editable ; FractionBox RowBox α - n + 1 m , FractionBox RowBox α - n + 2 m , , FractionBox RowBox α - n + m m , TagBox SubscriptBox b 1 HypergeometricPFQ Rule Editable , TagBox SubscriptBox b 2 HypergeometricPFQ Rule Editable , RowBox TagBox SubscriptBox b 3 HypergeometricPFQ Rule Editable ; TagBox SuperscriptBox z m HypergeometricPFQ Rule Editable ) /; RowBox RowBox m SuperscriptBox + RowBox n TraditionalForm [/itex]

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

 2001-10-29

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