html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 HypergeometricPFQ

 http://functions.wolfram.com/07.31.17.0013.01

 Input Form

 HypergeometricPFQ[{a, b, c, Subscript[a, 4], \[Ellipsis], Subscript[a, p]}, {d, e, Subscript[b, 3], \[Ellipsis], Subscript[b, q]}, z] - ((a b (d - c) (e - c))/(d e (a - c) (b - c))) HypergeometricPFQ[{a + 1, b + 1, c, Subscript[a, 4], \[Ellipsis], Subscript[a, p]}, {d + 1, e + 1, Subscript[b, 3], \[Ellipsis], Subscript[b, q]}, z] - ((a c (d - b) (e - b))/(d e (a - b) (c - b))) HypergeometricPFQ[{a + 1, b, c + 1, Subscript[a, 4], \[Ellipsis], Subscript[a, p]}, {d + 1, e + 1, Subscript[b, 3], \[Ellipsis], Subscript[b, q]}, z] - ((b c (d - a) (e - a))/(d e (b - a) (c - a))) HypergeometricPFQ[{a, b + 1, c + 1, Subscript[a, 4], \[Ellipsis], Subscript[a, p]}, {d + 1, e + 1, Subscript[b, 3], \[Ellipsis], Subscript[b, q]}, z] == 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["a", ",", "b", ",", "c", ",", SubscriptBox["a", "4"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List["d", ",", "e", ",", SubscriptBox["b", "3"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]], "-", RowBox[List[FractionBox[RowBox[List["a", " ", "b", RowBox[List["(", RowBox[List["d", "-", "c"]], ")"]], RowBox[List["(", RowBox[List["e", "-", "c"]], ")"]]]], RowBox[List["d", " ", "e", " ", RowBox[List["(", RowBox[List["a", "-", "c"]], ")"]], RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]]]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["a", "+", "1"]], ",", RowBox[List["b", "+", "1"]], ",", "c", ",", SubscriptBox["a", "4"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["d", "+", "1"]], ",", RowBox[List["e", "+", "1"]], ",", SubscriptBox["b", "3"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["a", " ", "c", RowBox[List["(", RowBox[List["d", "-", "b"]], ")"]], RowBox[List["(", RowBox[List["e", "-", "b"]], ")"]]]], RowBox[List["d", " ", "e", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], RowBox[List["(", RowBox[List["c", "-", "b"]], ")"]]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["a", "+", "1"]], ",", "b", ",", RowBox[List["c", "+", "1"]], ",", SubscriptBox["a", "4"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["d", "+", "1"]], ",", RowBox[List["e", "+", "1"]], ",", SubscriptBox["b", "3"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["b", " ", "c", RowBox[List["(", RowBox[List["d", "-", "a"]], ")"]], RowBox[List["(", RowBox[List["e", "-", "a"]], ")"]]]], RowBox[List["d", " ", "e", " ", RowBox[List["(", RowBox[List["b", "-", "a"]], ")"]], RowBox[List["(", RowBox[List["c", "-", "a"]], ")"]]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["a", ",", RowBox[List["b", "+", "1"]], ",", RowBox[List["c", "+", "1"]], ",", SubscriptBox["a", "4"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["d", "+", "1"]], ",", RowBox[List["e", "+", "1"]], ",", SubscriptBox["b", "3"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]]]]]], "\[Equal]", "0"]]]]

 MathML Form

 p F q ( a , b , c , a 4 , , a p ; d , e , b 3 , , b q ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List["a", ",", "b", ",", "c", ",", SubscriptBox["a", "4"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], ";", "d"]], ",", "e", ",", SubscriptBox["b", "3"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], ";", "z"]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] - a b ( d - c ) ( e - c ) d e ( a - c ) ( b - c ) p F q ( a + 1 , b + 1 , c , a 4 , , a p ; d + 1 , e + 1 , b 3 , , b q ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[RowBox[List["a", "+", "1"]], ",", RowBox[List["b", "+", "1"]], ",", "c", ",", SubscriptBox["a", "4"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], ";", RowBox[List["d", "+", "1"]]]], ",", RowBox[List["e", "+", "1"]], ",", SubscriptBox["b", "3"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], ";", "z"]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] - a c ( d - b ) ( e - b ) d e ( a - b ) ( c - b ) p F q ( a + 1 , b , c + 1 , a 4 , , a p ; d + 1 , e + 1 , b 3 , , b q ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[RowBox[List["a", "+", "1"]], ",", "b", ",", RowBox[List["c", "+", "1"]], ",", SubscriptBox["a", "4"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], ";", RowBox[List["d", "+", "1"]]]], ",", RowBox[List["e", "+", "1"]], ",", SubscriptBox["b", "3"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], ";", "z"]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] - b c ( d - a ) ( e - a ) d e ( b - a ) ( c - a ) p F q ( a , b + 1 , c + 1 , a 4 , , a p ; d + 1 , e + 1 , b 3 , , b q ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List["a", ",", RowBox[List["b", "+", "1"]], ",", RowBox[List["c", "+", "1"]], ",", SubscriptBox["a", "4"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], ";", RowBox[List["d", "+", "1"]]]], ",", RowBox[List["e", "+", "1"]], ",", SubscriptBox["b", "3"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], ";", "z"]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] 0 p F q ( a , b , c , a 4 , , a p ; d , e , b 3 , , b q ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List["a", ",", "b", ",", "c", ",", SubscriptBox["a", "4"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], ";", "d"]], ",", "e", ",", SubscriptBox["b", "3"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], ";", "z"]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] - a b ( d - c ) ( e - c ) d e ( a - c ) ( b - c ) p F q ( a + 1 , b + 1 , c , a 4 , , a p ; d + 1 , e + 1 , b 3 , , b q ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[RowBox[List["a", "+", "1"]], ",", RowBox[List["b", "+", "1"]], ",", "c", ",", SubscriptBox["a", "4"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], ";", RowBox[List["d", "+", "1"]]]], ",", RowBox[List["e", "+", "1"]], ",", SubscriptBox["b", "3"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], ";", "z"]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] - a c ( d - b ) ( e - b ) d e ( a - b ) ( c - b ) p F q ( a + 1 , b , c + 1 , a 4 , , a p ; d + 1 , e + 1 , b 3 , , b q ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[RowBox[List["a", "+", "1"]], ",", "b", ",", RowBox[List["c", "+", "1"]], ",", SubscriptBox["a", "4"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], ";", RowBox[List["d", "+", "1"]]]], ",", RowBox[List["e", "+", "1"]], ",", SubscriptBox["b", "3"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], ";", "z"]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] - b c ( d - a ) ( e - a ) d e ( b - a ) ( c - a ) p F q ( a , b + 1 , c + 1 , a 4 , , a p ; d + 1 , e + 1 , b 3 , , b q ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List["a", ",", RowBox[List["b", "+", "1"]], ",", RowBox[List["c", "+", "1"]], ",", SubscriptBox["a", "4"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], ";", RowBox[List["d", "+", "1"]]]], ",", RowBox[List["e", "+", "1"]], ",", SubscriptBox["b", "3"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], ";", "z"]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] 0 [/itex]

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

 2001-10-29