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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Differentiation > Low-order differentiation > With respect to z





http://functions.wolfram.com/07.27.20.0014.01









  


  








Input Form





D[HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z], {z, 2}] == ((Subscript[a, 1] (1 + Subscript[a, 1]) Subscript[a, 2] (1 + Subscript[a, 2]) Subscript[a, 3] (1 + Subscript[a, 3]))/ (Subscript[b, 1] (1 + Subscript[b, 1]) Subscript[b, 2] (1 + Subscript[b, 2]))) HypergeometricPFQ[{Subscript[a, 1] + 2, Subscript[a, 2] + 2, Subscript[a, 3] + 2}, {Subscript[b, 1] + 2, Subscript[b, 2] + 2}, z]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "2"]], "}"]]]]], 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_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["aa", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "1"]]], ")"]], " ", SubscriptBox["aa", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "2"]]], ")"]], " ", SubscriptBox["aa", "3"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "3"]]], ")"]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["aa", "1"], "+", "2"]], ",", RowBox[List[SubscriptBox["aa", "2"], "+", "2"]], ",", RowBox[List[SubscriptBox["aa", "3"], "+", "2"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["bb", "1"], "+", "2"]], ",", RowBox[List[SubscriptBox["bb", "2"], "+", "2"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List[SubscriptBox["bb", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "1"]]], ")"]], " ", SubscriptBox["bb", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "2"]]], ")"]]]]]]]]]


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





2001-10-29