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variants of this functions
HypergeometricPFQRegularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/07.32.20.0016.01









  


  










Input Form





D[z^\[Alpha] HypergeometricPFQRegularized[{-(n/r), (-n + 1)/r, \[Ellipsis], (-n + r - 1)/r, Subscript[a, r + 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z^m], {z, n}] == m^(n - \[Alpha] - 1/2) (2 Pi)^((m - 1)/2) Gamma[\[Alpha] + 1] z^(\[Alpha] - n) HypergeometricPFQRegularized[{-(n/r), (-n + 1)/r, \[Ellipsis], (-n + r - 1)/r, (\[Alpha] + 1)/m, (\[Alpha] + 2)/m, \[Ellipsis], (\[Alpha] + m)/m, Subscript[a, r + 1], \[Ellipsis], Subscript[a, p]}, {(\[Alpha] - n + 1)/m, (\[Alpha] - n + 2)/m, \[Ellipsis], (\[Alpha] - n + m)/m, Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z^m] /; Element[r, Integers] && r > 0 && Element[m, Integers] && m > 0 && Element[n, Integers] && n > 0










Standard Form





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MathML Form







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</ms> <ms> , </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> n </ms> </list> </apply> <ms> + </ms> <ms> r </ms> <ms> - </ms> <ms> 1 </ms> </list> </apply> <ms> r </ms> </apply> <ms> , </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> m </ms> </apply> <ms> , </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> + </ms> <ms> 2 </ms> </list> </apply> <ms> m </ms> </apply> <ms> , </ms> <ms> &#8230; </ms> <ms> , </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> + </ms> <ms> m </ms> </list> </apply> <ms> m </ms> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <apply> <ci> RowBox </ci> <list> <ms> r </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> </apply> <ms> , </ms> <ms> &#8230; </ms> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> p </ms> </apply> </list> </apply> <apply> <ci> InterpretTemplate </ci> <apply> <ci> Function </ci> <list> <apply> <ci> SlotSequence </ci> <cn type='integer'> 1 </cn> </apply> </list> </apply> </apply> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <ms> ; </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> - </ms> <ms> n </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> m </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> - </ms> <ms> n </ms> <ms> + </ms> <ms> 2 </ms> </list> </apply> <ms> m </ms> </apply> <ms> , </ms> <ms> &#8230; </ms> <ms> , </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> - </ms> <ms> n </ms> <ms> + </ms> <ms> m </ms> </list> </apply> <ms> m </ms> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> 1 </ms> </apply> <ms> , </ms> <ms> &#8230; </ms> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> q </ms> </apply> <ms> ; </ms> <apply> <ci> TagBox </ci> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <ms> m </ms> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> r </ms> <ms> &#8712; </ms> <apply> <ci> SuperscriptBox </ci> <ms> &#8469; </ms> <ms> + </ms> </apply> </list> </apply> <ms> &#8743; </ms> <apply> <ci> RowBox </ci> <list> <ms> m </ms> <ms> &#8712; </ms> <apply> <ci> SuperscriptBox </ci> <ms> &#8469; </ms> <ms> + </ms> </apply> </list> </apply> <ms> &#8743; </ms> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> &#8712; </ms> <apply> <ci> SuperscriptBox </ci> <ms> &#8469; </ms> <ms> + </ms> </apply> </list> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "n_"]], "}"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["z_", "\[Alpha]_"], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["n_", "r_"]]], ",", FractionBox[RowBox[List[RowBox[List["-", "n_"]], "+", "1"]], "r_"], ",", "\[Ellipsis]_", ",", FractionBox[RowBox[List[RowBox[List["-", "n_"]], "+", "r_", "-", "1"]], "r_"], ",", SubscriptBox["a_", RowBox[List["r_", "+", "1"]]], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "p_"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]], ",", SuperscriptBox["z_", "m_"]]], "]"]]]], ")"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["m", RowBox[List["n", "-", "\[Alpha]", "-", FractionBox["1", "2"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]], FractionBox[RowBox[List["m", "-", "1"]], "2"]], " ", RowBox[List["Gamma", "[", RowBox[List["\[Alpha]", "+", "1"]], "]"]], " ", SuperscriptBox["z", RowBox[List["\[Alpha]", "-", "n"]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["n", "r"]]], ",", FractionBox[RowBox[List[RowBox[List["-", "n"]], "+", "1"]], "r"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[RowBox[List["-", "n"]], "+", "r", "-", "1"]], "r"], ",", FractionBox[RowBox[List["\[Alpha]", "+", "1"]], "m"], ",", FractionBox[RowBox[List["\[Alpha]", "+", "2"]], "m"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["\[Alpha]", "+", "m"]], "m"], ",", SubscriptBox["a", RowBox[List["r", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["aa", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["\[Alpha]", "-", "n", "+", "1"]], "m"], ",", FractionBox[RowBox[List["\[Alpha]", "-", "n", "+", "2"]], "m"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["\[Alpha]", "-", "n", "+", "m"]], "m"], ",", SubscriptBox["bb", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["bb", "q"]]], "}"]], ",", SuperscriptBox["z", "m"]]], "]"]]]], "/;", RowBox[List[RowBox[List["r", "\[Element]", "Integers"]], "&&", RowBox[List["r", ">", "0"]], "&&", RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]










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





2001-10-29