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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/07.28.20.0026.01









  


  










Input Form





D[HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z], {z, n}] == (Product[Pochhammer[Subscript[a, j], n], {j, 1, 4}]/ Product[Pochhammer[Subscript[b, j], n], {j, 1, 3}]) HypergeometricPFQ[{Subscript[a, 1] + n, Subscript[a, 2] + n, Subscript[a, 3] + n, Subscript[a, 4] + n}, {Subscript[b, 1] + n, Subscript[b, 2] + n, Subscript[b, 3] + n}, z] /; 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[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "n_"]], "}"]]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", SubscriptBox["a_", "2"], ",", SubscriptBox["a_", "3"], ",", SubscriptBox["a_", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"], ",", SubscriptBox["b_", "3"]]], "}"]], ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "4"], RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["aa", "j"], ",", "n"]], "]"]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["aa", "1"], "+", "n"]], ",", RowBox[List[SubscriptBox["aa", "2"], "+", "n"]], ",", RowBox[List[SubscriptBox["aa", "3"], "+", "n"]], ",", RowBox[List[SubscriptBox["aa", "4"], "+", "n"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["bb", "1"], "+", "n"]], ",", RowBox[List[SubscriptBox["bb", "2"], "+", "n"]], ",", RowBox[List[SubscriptBox["bb", "3"], "+", "n"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "3"], RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["bb", "j"], ",", "n"]], "]"]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]










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





2001-10-29