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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.17.0024.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z] == SuperPlus[A][z] + SuperMinus[A][z] /; SuperPlus[A][z] == HypergeometricPFQ[{Subscript[a, 1]/2, Subscript[a, 2]/2, Subscript[a, 3]/2, (Subscript[a, 1] + 1)/2, (Subscript[a, 2] + 1)/2, (Subscript[a, 3] + 1)/2}, {1/2, Subscript[b, 1]/2, Subscript[b, 2]/2, (Subscript[b, 1] + 1)/2, (Subscript[b, 2] + 1)/2}, z^2] && SuperMinus[A][z] == ((z Product[Subscript[a, j], {j, 1, 3}])/ (Subscript[b, 1] Subscript[b, 2])) HypergeometricPFQ[ {(Subscript[a, 1] + 1)/2, (Subscript[a, 2] + 1)/2, (Subscript[a, 3] + 1)/2, (Subscript[a, 1] + 2)/2, (Subscript[a, 2] + 2)/2, (Subscript[a, 3] + 2)/2}, {3/2, (Subscript[b, 1] + 1)/2, (Subscript[b, 2] + 1)/2, (Subscript[b, 1] + 2)/2, (Subscript[b, 2] + 2)/2}, z^2]

 Standard Form

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 MathML Form

 3 F 2 ( a 1 , a 2 , a 3 ; b 1 , b 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[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]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], 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] A + ( z ) + A - ( z ) /; A + ( z ) 6 F 5 ( a 1 2 , a 2 2 , a 3 2 , a 1 + 1 2 , a 2 + 1 2 , a 3 + 1 2 ; 1 2 , b 1 2 , b 2 2 , b 1 + 1 2 , b 2 + 1 2 ; z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["6", TraditionalForm]], SubscriptBox["F", FormBox["5", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[SubscriptBox["a", "1"], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["a", "2"], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["a", "3"], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "1"], "+", "1"]], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "2"], "+", "1"]], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "3"], "+", "1"]], "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["b", "1"], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["b", "2"], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "1"]], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", "2"], "+", "1"]], "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[SuperscriptBox["z", "2"], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] A - ( z ) z j = 1 3 a j b 1 b 2 6 F 5 ( a 1 + 1 2 , a 2 + 1 2 , a 3 + 1 2 , a 1 + 2 2 , a 2 + 2 2 , a 3 + 2 2 ; 3 2 , b 1 + 1 2 , b 2 + 1 2 , b 1 + 2 2 , b 2 + 2 2 ; z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["6", TraditionalForm]], SubscriptBox["F", FormBox["5", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[SubscriptBox["a", "1"], "+", "1"]], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "2"], "+", "1"]], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "3"], "+", "1"]], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "1"], "+", "2"]], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "2"], "+", "2"]], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "3"], "+", "2"]], "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "1"]], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", "2"], "+", "1"]], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "2"]], "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", "2"], "+", "2"]], "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[SuperscriptBox["z", "2"], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] Condition HypergeometricPFQ Subscript a 1 Subscript a 2 Subscript a 3 Subscript b 1 Subscript b 2 z SuperPlus A z SuperMinus A z SuperPlus A z HypergeometricPFQ Subscript a 1 2 -1 Subscript a 2 2 -1 Subscript a 3 2 -1 Subscript a 1 1 2 -1 Subscript a 2 1 2 -1 Subscript a 3 1 2 -1 1 2 Subscript b 1 2 -1 Subscript b 2 2 -1 Subscript b 1 1 2 -1 Subscript b 2 1 2 -1 z 2 SuperMinus A z z j 1 3 Subscript a j Subscript b 1 Subscript b 2 -1 HypergeometricPFQ Subscript a 1 1 2 -1 Subscript a 2 1 2 -1 Subscript a 3 1 2 -1 Subscript a 1 2 2 -1 Subscript a 2 2 2 -1 Subscript a 3 2 2 -1 3 2 Subscript b 1 1 2 -1 Subscript b 2 1 2 -1 Subscript b 1 2 2 -1 Subscript b 2 2 2 -1 z 2 [/itex]

 Rule Form

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

 2001-10-29