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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.31.20.0007.01









  


  








Input Form





D[HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z], z] == (Product[Subscript[a, j], {j, 1, p}]/Product[Subscript[b, j], {j, 1, q}]) HypergeometricPFQ[{Subscript[a, 1] + 1, \[Ellipsis], Subscript[a, p] + 1}, {Subscript[b, 1] + 1, \[Ellipsis], Subscript[b, q] + 1}, z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], 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[FractionBox[RowBox[List[" ", 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[RowBox[List[SubscriptBox["a", "1"], "+", "1"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], "+", "1"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["b", "1"], "+", "1"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], "+", "1"]]]], "}"]], ",", "z"]], "]"]]]]]]]]








MathML Form







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





2001-10-29