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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.25.20.0006.01









  


  








Input Form





Derivative[{0, 1}, {0, 0}, 0][HypergeometricPFQ][ {Subscript[a, 1], Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2]}, z] == Sum[(Pochhammer[Subscript[a, 1], k]/(Pochhammer[Subscript[b, 1], k] Pochhammer[Subscript[b, 2], k] k!)) D[Pochhammer[Subscript[a, 2], k], {Subscript[a, 2], n}] z^k, {k, 0, Infinity}] /; Element[n, Integers] && n > 0








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["HypergeometricPFQ", TagBox[RowBox[List["(", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", "0"]], "}"]], ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", SubscriptBox["a_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["aa", "1"], ",", "k"]], "]"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["aa", "2"], ",", "n"]], "}"]]]]], RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["aa", "2"], ",", "k"]], "]"]]]], " ", SuperscriptBox["z", "k"]]], RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["bb", "1"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["bb", "2"], ",", "k"]], "]"]], " ", RowBox[List["k", "!"]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]


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





2001-10-29