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/07.22.13.0002.01

 Input Form

 z^2 Derivative[3][w][z] + (Subscript[b, 1] + Subscript[b, 2] + 1) z Derivative[2][w][z] + (Subscript[b, 1] Subscript[b, 2] - z) Derivative[1][w][z] - Subscript[a, 1] w[z] == 0 /; w[z] == Subscript[c, 1] HypergeometricPFQRegularized[{Subscript[a, 1]}, {Subscript[b, 1], Subscript[b, 2]}, z] + Subscript[c, 2] (MeijerG[{{1 - Subscript[a, 1]}, {}}, {{0, 1 - Subscript[b, 1]}, {1 - Subscript[b, 2]}}, z] + MeijerG[{{1 - Subscript[a, 1]}, {}}, {{0, 1 - Subscript[b, 2]}, {1 - Subscript[b, 1]}}, z]) + Subscript[c, 3] MeijerG[{{1 - Subscript[a, 1]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}, {}}, -z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"], "+", "1"]], ")"]], " ", "z", " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["b", "1"], " ", SubscriptBox["b", "2"]]], "-", "z"]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], "-", RowBox[List[SubscriptBox["a", "1"], " ", RowBox[List["w", "[", "z", "]"]]]]]], "\[Equal]", "0"]], " ", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["c", "1"], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", SubscriptBox["a", "1"], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"]]], "}"]], ",", "z"]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", SubscriptBox["a", "1"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", SubscriptBox["b", "2"]]], "}"]]]], "}"]], ",", "z"]], "]"]], "+", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", SubscriptBox["a", "1"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", SubscriptBox["b", "1"]]], "}"]]]], "}"]], ",", "z"]], "]"]]]], ")"]]]], "+", RowBox[List[SubscriptBox["c", "3"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", SubscriptBox["a", "1"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]]]]]]]]]]]]

 MathML Form

 w ( 3 ) TagBox[RowBox[List["(", "3", ")"]], Derivative] ( z ) z 2 + ( b 1 + b 2 + 1 ) w ′′ ( z ) z - a 1 w ( z ) + ( b 1 b 2 - z ) w ( z ) 0 /; w ( z ) c 1 1 F ~ 2 ( a 1 ; b 1 , b 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "1"], SubscriptBox[OverscriptBox["F", "~"], "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[SubscriptBox["a", "1"], 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] + c 2 ( G 1 , 3 2 , 1 ( z 1 - a 1 0 , 1 - b 1 , 1 - b 2 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["1", ",", "3"]], RowBox[List["2", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] + G 1 , 3 2 , 1 ( z 1 - a 1 0 , 1 - b 2 , 1 - b 1 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["1", ",", "3"]], RowBox[List["2", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] ) + c 3 G 1 , 3 3 , 1 ( - z 1 - a 1 0 , 1 - b 1 , 1 - b 2 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["1", ",", "3"]], RowBox[List["3", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["-", "z"]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] Condition z 3 w z z 2 Subscript b 1 Subscript b 2 1 z 2 w z z -1 Subscript a 1 w z Subscript b 1 Subscript b 2 -1 z z w z 0 w z Subscript c 1 HypergeometricPFQRegularized Subscript a 1 Subscript b 1 Subscript b 2 z Subscript c 2 MeijerG 1 -1 Subscript a 1 0 1 -1 Subscript b 1 1 -1 Subscript b 2 z MeijerG 1 -1 Subscript a 1 0 1 -1 Subscript b 2 1 -1 Subscript b 1 z Subscript c 3 MeijerG 1 -1 Subscript a 1 0 1 -1 Subscript b 1 1 -1 Subscript b 2 -1 z [/itex]

 Rule Form

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

 2007-05-02