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 HypergeometricPFQ

 http://functions.wolfram.com/07.31.17.0020.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] == SuperPlus[A][z] + SuperMinus[A][z] /; SuperPlus[A][z] == HypergeometricPFQ[{Subscript[a, 1]/2, \[Ellipsis], Subscript[a, p]/2, (Subscript[a, 1] + 1)/2, \[Ellipsis], (Subscript[a, p] + 1)/2}, {1/2, Subscript[b, 1]/2, \[Ellipsis], Subscript[b, q]/2, (Subscript[b, 1] + 1)/2, \[Ellipsis], (Subscript[b, q] + 1)/2}, 4^(p - q - 1) z^2] && SuperMinus[A][z] == ((z Product[Subscript[a, j], {j, 1, p}])/ Product[Subscript[b, j], {j, 1, q}]) HypergeometricPFQ[ {(Subscript[a, 1] + 1)/2, \[Ellipsis], (Subscript[a, p] + 1)/2, (Subscript[a, 1] + 2)/2, \[Ellipsis], (Subscript[a, p] + 2)/2}, {3/2, (Subscript[b, 1] + 1)/2, \[Ellipsis], (Subscript[b, q] + 1)/2, (Subscript[b, 1] + 2)/2, \[Ellipsis], (Subscript[b, q] + 2)/2}, 4^(p - q - 1) z^2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox["A", "+"], "[", "z", "]"]], "+", RowBox[List[SuperscriptBox["A", "-"], "[", "z", "]"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["A", "+"], "[", "z", "]"]], "\[Equal]", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[SubscriptBox["a", "1"], "2"], ",", "\[Ellipsis]", ",", FractionBox[SubscriptBox["a", "p"], "2"], ",", FractionBox[RowBox[List[SubscriptBox["a", "1"], "+", "1"]], "2"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["a", "p"], "+", "1"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox[SubscriptBox["b", "1"], "2"], ",", "\[Ellipsis]", ",", FractionBox[SubscriptBox["b", "q"], "2"], ",", FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "1"]], "2"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["b", "q"], "+", "1"]], "2"]]], "}"]], ",", RowBox[List[SuperscriptBox["4", RowBox[List["p", "-", "q", "-", "1"]]], SuperscriptBox["z", "2"]]]]], "]"]]]], "\[And]", RowBox[List[RowBox[List[SuperscriptBox["A", "-"], "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["z", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], SubscriptBox["a", "j"]]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], SubscriptBox["b", "j"]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List[SubscriptBox["a", "1"], "+", "1"]], "2"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["a", "p"], "+", "1"]], "2"], ",", FractionBox[RowBox[List[SubscriptBox["a", "1"], "+", "2"]], "2"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["a", "p"], "+", "2"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "1"]], "2"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["b", "q"], "+", "1"]], "2"], ",", FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "2"]], "2"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["b", "q"], "+", "2"]], "2"]]], "}"]], ",", RowBox[List[SuperscriptBox["4", RowBox[List["p", "-", "q", "-", "1"]]], SuperscriptBox["z", "2"]]]]], "]"]]]]]]]]]]]]

 MathML Form

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

 2001-10-29