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/07.31.10.0001.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] == 1 + (z Product[Subscript[a, k]/Product[Subscript[b, k], {k, 1, q}], {k, 1, p}])/(1 + -((z Product[1 + Subscript[a, j], {j, 1, p}])/ (2 Product[1 + Subscript[b, j], {j, 1, q}]))/ (1 + (z Product[1 + Subscript[a, j], {j, 1, p}])/ (2 Product[1 + Subscript[b, j], {j, 1, q}]) - (z Product[2 + Subscript[a, j], {j, 1, p}])/ (3 Product[2 + Subscript[b, j], {j, 1, q}])/ (1 + (z Product[2 + Subscript[a, j], {j, 1, p}])/ (3 Product[2 + Subscript[b, j], {j, 1, q}]) + \[Ellipsis])))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["1", "+", RowBox[List[RowBox[List["(", RowBox[List["z", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "p"], RowBox[List[SubscriptBox["a", "k"], "/", RowBox[List["(", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "q"], SubscriptBox["b", "k"]]], ")"]]]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["1", "+", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "j"]]], ")"]]]]]]]]], "/", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "j"]]], ")"]]]]]]], "+", FractionBox[RowBox[List["-", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List["3", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["(", RowBox[List["2", "+", SubscriptBox["b", "j"]]], ")"]]]]]]]]], RowBox[List["1", "+", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List["3", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["(", RowBox[List["2", "+", SubscriptBox["b", "j"]]], ")"]]]]]]], "+", "\[Ellipsis]"]]]]], ")"]]]]]], ")"]]]]]]]]]]

 MathML Form

 p F q ( a 1 , , a p ; b 1 , , b q ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] 1 + ( z k = 1 p a k / ( k = 1 q b k ) ) / ( 1 + - z j = 1 p ( 1 + a j ) 2 j = 1 q ( 1 + b j ) / ( 1 + z j = 1 p ( 1 + a j ) 2 j = 1 q ( 1 + b j ) + - z j = 1 p ( 2 + a j ) 3 j = 1 q ( 2 + b j ) 1 + z j = 1 p ( 2 + a j ) 3 j = 1 q ( 2 + b j ) + ) ) HypergeometricPFQ Subscript a 1 Subscript a p Subscript b 1 Subscript b q z 1 z k 1 p Subscript a k k 1 q Subscript b k -1 1 -1 z j 1 p 1 Subscript a j 2 j 1 q 1 Subscript b j -1 1 z j 1 p 1 Subscript a j 2 j 1 q 1 Subscript b j -1 -1 z j 1 p 2 Subscript a j 3 j 1 q 2 Subscript b j -1 1 z j 1 p 2 Subscript a j 3 j 1 q 2 Subscript b j -1 -1 -1 -1 [/itex]

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

 2001-10-29