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/07.27.13.0005.01

 Input Form

 Wronskian[HypergeometricPFQRegularized[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z], z^(1 - Subscript[b, 1]) HypergeometricPFQRegularized[ {1 + Subscript[a, 1] - Subscript[b, 1], 1 + Subscript[a, 2] - Subscript[b, 1], 1 + Subscript[a, 3] - Subscript[b, 1]}, {2 - Subscript[b, 1], 1 - Subscript[b, 1] + Subscript[b, 2]}, z], z^(1 - Subscript[b, 2]) HypergeometricPFQRegularized[ {1 + Subscript[a, 1] - Subscript[b, 2], 1 + Subscript[a, 2] - Subscript[b, 2], 1 + Subscript[a, 3] - Subscript[b, 2]}, {2 - Subscript[b, 2], 1 + Subscript[b, 1] - Subscript[b, 2]}, z], z] == ((Sin[Pi Subscript[b, 1]] Sin[Pi (Subscript[b, 1] - Subscript[b, 2])] Sin[Pi Subscript[b, 2]])/Pi^3) (1 - z)^(-2 - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3] + Subscript[b, 1] + Subscript[b, 2]) z^(-1 - Subscript[b, 1] - Subscript[b, 2])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", SubscriptBox["a", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"]]], "}"]], ",", "z"]], "]"]], ",", RowBox[List[SuperscriptBox["z", RowBox[List["1", "-", SubscriptBox["b", "1"]]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "2"], "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "3"], "-", SubscriptBox["b", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"]]]]], "}"]], ",", "z"]], "]"]]]], ",", " ", RowBox[List[SuperscriptBox["z", RowBox[List["1", "-", SubscriptBox["b", "2"]]]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "2"], "-", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "3"], "-", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]]]], "}"]], ",", "z"]], "]"]]]], ",", " ", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", SubscriptBox["b", "1"]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]], ")"]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", SubscriptBox["b", "2"]]], "]"]]]], SuperscriptBox["\[Pi]", "3"]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", SubscriptBox["a", "1"], "-", SubscriptBox["a", "2"], "-", SubscriptBox["a", "3"], "+", SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"]]]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "-", SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]]]]]]]]]

 MathML Form

 W z ( 3 F ~ 2 ( a 1 , a 2 , a 3 ; b 1 , b 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox[OverscriptBox["F", "~"], "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] , z 1 - b 1 3 F ~ 2 ( a 1 - b 1 + 1 , a 2 - b 1 + 1 , a 3 - b 1 + 1 ; 2 - b 1 , - b 1 + b 2 + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox[OverscriptBox["F", "~"], "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["b", "1"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["b", "1"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "3"], "-", SubscriptBox["b", "1"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["2", "-", SubscriptBox["b", "1"]]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", SubscriptBox["b", "1"]]], "+", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] , z 1 - b 2 3 F ~ 2 ( a 1 - b 2 + 1 , a 2 - b 2 + 1 , a 3 - b 2 + 1 ; 2 - b 2 , b 1 - b 2 + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox[OverscriptBox["F", "~"], "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "3"], "-", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["2", "-", SubscriptBox["b", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] ) sin ( π b 1 ) sin ( π ( b 1 - b 2 ) ) sin ( π b 2 ) π 3 ( 1 - z ) - a 1 - a 2 - a 3 + b 1 + b 2 - 2 z - b 1 - b 2 - 1 Subscript W z HypergeometricPFQRegularized Subscript a 1 Subscript a 2 Subscript a 3 Subscript b 1 Subscript b 2 z z 1 -1 Subscript b 1 HypergeometricPFQRegularized Subscript a 1 -1 Subscript b 1 1 Subscript a 2 -1 Subscript b 1 1 Subscript a 3 -1 Subscript b 1 1 2 -1 Subscript b 1 -1 Subscript b 1 Subscript b 2 1 z z 1 -1 Subscript b 2 HypergeometricPFQRegularized Subscript a 1 -1 Subscript b 2 1 Subscript a 2 -1 Subscript b 2 1 Subscript a 3 -1 Subscript b 2 1 2 -1 Subscript b 2 Subscript b 1 -1 Subscript b 2 1 z Subscript b 1 Subscript b 1 -1 Subscript b 2 Subscript b 2 3 -1 1 -1 z -1 Subscript a 1 -1 Subscript a 2 -1 Subscript a 3 Subscript b 1 Subscript b 2 -2 z -1 Subscript b 1 -1 Subscript b 2 -1 [/itex]

 Rule Form

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

 2007-05-02

© 1998-2013 Wolfram Research, Inc.