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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/07.32.03.0008.01









  


  








Input Form





HypergeometricPFQRegularized[{a, b, Subscript[a, 3], \[Ellipsis], Subscript[a, p]}, {a + 1, b + 1, Subscript[b, 3], \[Ellipsis], Subscript[b, q]}, z] == (1/(a - b)) ((1/Gamma[a]) HypergeometricPFQRegularized[{b, Subscript[a, 3], \[Ellipsis], Subscript[a, p]}, {b + 1, Subscript[b, 3], \[Ellipsis], Subscript[b, q]}, z] - (1/Gamma[b]) HypergeometricPFQRegularized[ {a, Subscript[a, 3], \[Ellipsis], Subscript[a, p]}, {a + 1, Subscript[b, 3], \[Ellipsis], Subscript[b, q]}, z]) /; a != b








Standard Form





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MathML Form







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</ms> <apply> <ci> RowBox </ci> <list> <ms> a </ms> <ms> &#8800; </ms> <ms> b </ms> </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["a_", ",", "b_", ",", SubscriptBox["a_", "3"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "p_"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["a_", "+", "1"]], ",", RowBox[List["b_", "+", "1"]], ",", SubscriptBox["b_", "3"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[FractionBox[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["b", ",", SubscriptBox["aa", "3"], ",", "\[Ellipsis]", ",", SubscriptBox["aa", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["b", "+", "1"]], ",", SubscriptBox["bb", "3"], ",", "\[Ellipsis]", ",", SubscriptBox["bb", "q"]]], "}"]], ",", "z"]], "]"]], RowBox[List["Gamma", "[", "a", "]"]]], "-", FractionBox[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["a", ",", SubscriptBox["aa", "3"], ",", "\[Ellipsis]", ",", SubscriptBox["aa", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["a", "+", "1"]], ",", SubscriptBox["bb", "3"], ",", "\[Ellipsis]", ",", SubscriptBox["bb", "q"]]], "}"]], ",", "z"]], "]"]], RowBox[List["Gamma", "[", "b", "]"]]]]], RowBox[List["a", "-", "b"]]], "/;", RowBox[List["a", "\[NotEqual]", "b"]]]]]]]]


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





2001-10-29