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 HypergeometricPFQ

 http://functions.wolfram.com/07.28.20.0002.01

 Input Form

 Derivative[{1, 0, 0, 0}, {0, 0, 0}, 0][HypergeometricPFQ][ {Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] == ((z Product[Subscript[a, j], {j, 2, 4}])/Product[Subscript[b, j], {j, 1, 3}]) HypergeometricPFQ[{{1 + Subscript[a, 1], 1 + Subscript[a, 2], 1 + Subscript[a, 3], 1 + Subscript[a, 4]}, {1}, {1, Subscript[a, 1]}}, {{2, 1 + Subscript[b, 1], 1 + Subscript[b, 2], 1 + Subscript[b, 3]}, {}, {1 + Subscript[a, 1]}}, z, z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["Derivative", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "0", ",", "0", ",", "0"]], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", "0", ",", "0"]], "}"]], ",", "0"]], "]"]], "[", "HypergeometricPFQ", "]"]], "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", SubscriptBox["a", "3"], ",", SubscriptBox["a", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"], ",", SubscriptBox["b", "3"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "2"]], "4"], SubscriptBox["a", "j"]]]]], RowBox[List[" ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "3"], SubscriptBox["b", "j"]]]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", SubscriptBox["a", "1"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", ",", RowBox[List["1", "+", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["b", "3"]]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["1", "+", SubscriptBox["a", "1"]]], "}"]]]], "}"]], ",", "z", ",", "z"]], "]"]]]]]]]]

 MathML Form

 4 F 3 ( { 1 , 0 , 0 , 0 } , { 0 , 0 , 0 } , 0 ) ( a 1 , a 2 , a 3 TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]] , a 4 TagBox[SubscriptBox["a", "4"], HypergeometricPFQ, Rule[Editable, True]] ; b 1 , b 2 , b 3 TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "2"], ",", TagBox[SubscriptBox["b", "3"], HypergeometricPFQ, Rule[Editable, True]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]] ; z TagBox["z", HypergeometricPFQ, Rule[Editable, True]] ) z j = 2 4 a j j = 1 3 b j F 4 0 1 4 1 2 ( a 1 + 1 , a 2 + 1 , a 3 + 1 , a 4 + 1 ; 1 ; 1 , a 1 ; 2 , b 1 + 1 , b 2 + 1 , b 3 + 1 ; ; a 1 + 1 ; z , z ) 4 F 3 ( { 1 , 0 , 0 , 0 } , { 0 , 0 , 0 } , 0 ) ( a 1 , a 2 , a 3 TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]] , a 4 TagBox[SubscriptBox["a", "4"], HypergeometricPFQ, Rule[Editable, True]] ; b 1 , b 2 , b 3 TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "2"], ",", TagBox[SubscriptBox["b", "3"], HypergeometricPFQ, Rule[Editable, True]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]] ; z TagBox["z", HypergeometricPFQ, Rule[Editable, True]] ) z j = 2 4 a j j = 1 3 b j F 4 0 1 4 1 2 ( a 1 + 1 , a 2 + 1 , a 3 + 1 , a 4 + 1 ; 1 ; 1 , a 1 ; 2 , b 1 + 1 , b 2 + 1 , b 3 + 1 ; ; a 1 + 1 ; z , z ) [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["HypergeometricPFQ", TagBox[RowBox[List["(", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "0", ",", "0", ",", "0"]], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", "0", ",", "0"]], "}"]], ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", SubscriptBox["a_", "2"], ",", SubscriptBox["a_", "3"], ",", SubscriptBox["a_", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"], ",", SubscriptBox["b_", "3"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "2"]], "4"], SubscriptBox["aa", "j"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["aa", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["aa", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["aa", "3"]]], ",", RowBox[List["1", "+", SubscriptBox["aa", "4"]]]]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", SubscriptBox["aa", "1"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", ",", RowBox[List["1", "+", SubscriptBox["bb", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["bb", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["bb", "3"]]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["1", "+", SubscriptBox["aa", "1"]]], "}"]]]], "}"]], ",", "z", ",", "z"]], "]"]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "3"], SubscriptBox["bb", "j"]]]]]]]]

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

 2001-10-29