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variants of this functions
HypergeometricPFQRegularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Specific values > Specialized values > Case pF~qwith fixed a1, ..., ap





http://functions.wolfram.com/07.32.03.0006.01









  


  










Input Form





HypergeometricPFQRegularized[{1, Subscript[a, 2], \[Ellipsis], Subscript[a, p]}, {3, Subscript[b, 2], \[Ellipsis], Subscript[b, q]}, z] == (1/z^2) (1/Product[(Subscript[a, j] - 2) (Subscript[a, j] - 1), {j, 2, p}]) (HypergeometricPFQRegularized[{Subscript[a, 2] - 2, \[Ellipsis], Subscript[a, p] - 2}, {Subscript[b, 2] - 2, \[Ellipsis], Subscript[b, q] - 2}, z] - (z Product[Subscript[a, j] - 2, {j, 2, p}])/ Product[Gamma[Subscript[b, j] - 1], {j, 2, q}] - 1/Product[Gamma[Subscript[b, j] - 2], {j, 2, q}])










Standard Form





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MathML Form







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</ms> <apply> <ci> RowBox </ci> <list> <ms> j </ms> <ms> = </ms> <ms> 2 </ms> </list> </apply> <ms> q </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> &#915; </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> j </ms> </apply> <ms> - </ms> <ms> 2 </ms> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </apply> </list> </apply> <ms> ) </ms> </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["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", SubscriptBox["a_", "2"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "p_"]]], "}"]], ",", RowBox[List["{", RowBox[List["3", ",", SubscriptBox["b_", "2"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["aa", "2"], "-", "2"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["aa", "p"], "-", "2"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["bb", "2"], "-", "2"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["bb", "q"], "-", "2"]]]], "}"]], ",", "z"]], "]"]], "-", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "2"]], "p"], RowBox[List["(", RowBox[List[SubscriptBox["a", "j"], "-", "2"]], ")"]]]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "2"]], "q"], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["b", "j"], "-", "1"]], "]"]]]]], "-", FractionBox["1", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "2"]], "q"], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["b", "j"], "-", "2"]], "]"]]]]]]], RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "2"]], "p"], RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["a", "j"], "-", "2"]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["a", "j"], "-", "1"]], ")"]]]]]]]]]]]]]










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





2001-10-29





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