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variants of this functions
HypergeometricPFQRegularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > General characteristics > Some abbreviations





http://functions.wolfram.com/07.32.04.0001.01









  


  








Input Form





NonTerminatingHypergeometricSeriesQ[{Subscript[a, 1], Subscript[a, 2], \[Ellipsis], Subscript[a, p]}] == ( !((Element[-Subscript[a, 1], Integers] && -Subscript[a, 1] >= 0) || \[Ellipsis] || (Element[-Subscript[a, p], Integers] && -Subscript[a, p] >= 0)))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["NonTerminatingHypergeometricSeriesQ", "[", RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], "]"]], "\[Equal]", RowBox[List["Not", "[", RowBox[List[RowBox[List[RowBox[List["Element", "[", RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], ",", "Integers"]], "]"]], "\[And]", RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], "\[GreaterEqual]", "0"]]]], "\[Or]", "\[Ellipsis]", "\[Or]", RowBox[List[RowBox[List["Element", "[", RowBox[List[RowBox[List["-", SubscriptBox["a", "p"]]], ",", "Integers"]], "]"]], "\[And]", RowBox[List[RowBox[List["-", SubscriptBox["a", "p"]]], "\[GreaterEqual]", "0"]]]]]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> &#119977;&#119983; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> { </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> <mo> } </mo> </mrow> <mo> ) </mo> </mrow> <mo> = </mo> <mrow> <mo> &#172; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8744; </mo> <mo> &#8230; </mo> <mo> &#8744; </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Set </ci> <apply> <ci> &#119977;&#119983; </ci> <list> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> p </ci> </apply> </list> </apply> <apply> <not /> <apply> <or /> <apply> <in /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <ci> &#8469; </ci> </apply> <ci> &#8230; </ci> <apply> <in /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> p </ci> </apply> </apply> <ci> &#8469; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["NonTerminatingHypergeometricSeriesQ", "[", RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", SubscriptBox["a_", "2"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "p_"]]], "}"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SubscriptBox["aa", "1"]]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", SubscriptBox["aa", "1"]]], "\[GreaterEqual]", "0"]]]], ")"]], "||", "\[Ellipsis]", "||", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SubscriptBox["aa", "p"]]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", SubscriptBox["aa", "p"]]], "\[GreaterEqual]", "0"]]]], ")"]]]], ")"]]]]]]]]


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





2001-10-29