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 HypergeometricPFQ

 http://functions.wolfram.com/07.22.13.0010.01

 Input Form

 Wronskian[h[z] HypergeometricPFQRegularized[{Subscript[a, 1]}, {Subscript[b, 1], Subscript[b, 2]}, g[z]], h[z] (MeijerG[{{1 - Subscript[a, 1]}, {}}, {{0, 1 - Subscript[b, 1]}, {1 - Subscript[b, 2]}}, g[z]] + MeijerG[{{1 - Subscript[a, 1]}, {}}, {{0, 1 - Subscript[b, 2]}, {1 - Subscript[b, 1]}}, g[z]]), h[z] MeijerG[{{1 - Subscript[a, 1]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}, {}}, -g[z]], z] == (-g[z])^(-Subscript[b, 1] - Subscript[b, 2]) g[z]^(-1 - Subscript[b, 1] - Subscript[b, 2]) ((-g[z])^Subscript[b, 2] g[z]^Subscript[b, 1] + (-g[z])^Subscript[b, 1] g[z]^Subscript[b, 2]) Gamma[1 + Subscript[a, 1] - Subscript[b, 1]] Gamma[1 + Subscript[a, 1] - Subscript[b, 2]] Derivative[1][g][z]^3 h[z]^3

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[RowBox[List["h", "[", "z", "]"]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", SubscriptBox["a", "1"], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"]]], "}"]], ",", RowBox[List["g", "[", "z", "]"]]]], "]"]]]], ",", " ", RowBox[List[RowBox[List["h", "[", "z", "]"]], 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"]]], "}"]]]], "}"]], ",", RowBox[List["g", "[", "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"]]], "}"]]]], "}"]], ",", RowBox[List["g", "[", "z", "]"]]]], "]"]]]], ")"]]]], ",", " ", RowBox[List[RowBox[List["h", "[", "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", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["-", RowBox[List["g", "[", "z", "]"]]]]]], "]"]]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", RowBox[List["g", "[", "z", "]"]]]], ")"]], RowBox[List[RowBox[List["-", SubscriptBox["b", "1"]]], "-", SubscriptBox["b", "2"]]]], " ", SuperscriptBox[RowBox[List["g", "[", "z", "]"]], RowBox[List[RowBox[List["-", "1"]], "-", SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", RowBox[List["g", "[", "z", "]"]]]], ")"]], SubscriptBox["b", "2"]], " ", SuperscriptBox[RowBox[List["g", "[", "z", "]"]], SubscriptBox["b", "1"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", RowBox[List["g", "[", "z", "]"]]]], ")"]], SubscriptBox["b", "1"]], " ", SuperscriptBox[RowBox[List["g", "[", "z", "]"]], SubscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["b", "1"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["b", "2"]]], "]"]], SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "3"], SuperscriptBox[RowBox[List["h", "[", "z", "]"]], "3"]]]]]]]

 MathML Form

 W z ( h ( z ) 1 F ~ 2 ( a 1 ; b 1 , b 2 ; g ( 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[RowBox[List["g", "(", "z", ")"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] , h ( z ) ( G 1 , 3 2 , 1 ( g ( 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[RowBox[List["g", "(", "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 ( g ( 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[RowBox[List["g", "(", "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]] ) , h ( z ) G 1 , 3 3 , 1 ( - g ( 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["-", RowBox[List["g", "(", "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 ( z ) ) - b 1 - b 2 g ( z ) - b 1 - b 2 - 1 ( g ( z ) b 2 ( - g ( z ) ) b 1 + g ( z ) b 1 ( - g ( z ) ) b 2 ) Γ ( a 1 - b 1 + 1 ) Γ ( a 1 - b 2 + 1 ) g ( z ) 3 h ( z ) 3 Subscript W z h z HypergeometricPFQRegularized Subscript a 1 Subscript b 1 Subscript b 2 g z h z MeijerG 1 -1 Subscript a 1 0 1 -1 Subscript b 1 1 -1 Subscript b 2 g z MeijerG 1 -1 Subscript a 1 0 1 -1 Subscript b 2 1 -1 Subscript b 1 g z h z MeijerG 1 -1 Subscript a 1 0 1 -1 Subscript b 1 1 -1 Subscript b 2 -1 g z -1 g z -1 Subscript b 1 -1 Subscript b 2 g z -1 Subscript b 1 -1 Subscript b 2 -1 g z Subscript b 2 -1 g z Subscript b 1 g z Subscript b 1 -1 g z Subscript b 2 Gamma Subscript a 1 -1 Subscript b 1 1 Gamma Subscript a 1 -1 Subscript b 2 1 z g z 3 h z 3 [/itex]

 Rule Form

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

 2007-05-02

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