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 HypergeometricPFQ

 http://functions.wolfram.com/07.28.17.0016.01

 Input Form

 HypergeometricPFQ[{a + 1, b + 1, Subscript[a, 3], Subscript[a, 4]}, {c + 1, d + 1, e + 1}, z] - ((c d (a - e) (b - e))/(a b (c - e) (d - e))) HypergeometricPFQ[{a, b, Subscript[a, 3], Subscript[a, 4]}, {c, d, e + 1}, z] - ((c e (a - d) (b - d))/(a b (c - d) (e - d))) HypergeometricPFQ[{a, b, Subscript[a, 3], Subscript[a, 4]}, {c, d + 1, e}, z] - ((d e (a - c) (b - c))/(a b (d - c) (e - c))) HypergeometricPFQ[{a, b, Subscript[a, 3], Subscript[a, 4]}, {c + 1, d, e}, z] == 0

 Standard Form

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 MathML Form

 4 F 3 ( a + 1 , b + 1 , a 3 , a 4 ; c + 1 , d + 1 , e + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["a", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["b", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["c", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["d", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["e", "+", "1"]], 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] - d e ( a - c ) ( b - c ) a b ( d - c ) ( e - c ) 4 F 3 ( a , b , a 3 , a 4 ; c + 1 , d , e ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["b", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["c", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["d", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["e", 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] - c e ( a - d ) ( b - d ) a b ( c - d ) ( e - d ) 4 F 3 ( a , b , a 3 , a 4 ; c , d + 1 , e ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["b", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["c", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["d", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["e", 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] - c d ( a - e ) ( b - e ) a b ( c - e ) ( d - e ) 4 F 3 ( a , b , a 3 , a 4 ; c , d , e + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["b", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["c", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["d", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["e", "+", "1"]], 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] 0 HypergeometricPFQ a 1 b 1 Subscript a 3 Subscript a 4 c 1 d 1 e 1 z -1 d e a -1 c b -1 c a b d -1 c e -1 c -1 HypergeometricPFQ a b Subscript a 3 Subscript a 4 c 1 d e z -1 c e a -1 d b -1 d a b c -1 d e -1 d -1 HypergeometricPFQ a b Subscript a 3 Subscript a 4 c d 1 e z -1 c d a -1 e b -1 e a b c -1 e d -1 e -1 HypergeometricPFQ a b Subscript a 3 Subscript a 4 c d e 1 z 0 [/itex]

 Rule Form

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

 2001-10-29