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/07.27.17.0004.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {b, Subscript[b, 2]}, z] == ((Subscript[B, 1] + Subscript[C, 1] z)/z) HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {b - 1, Subscript[b, 2]}, z] + ((Subscript[B, 2] + Subscript[C, 2] z)/z) HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {b - 2, Subscript[b, 2]}, z] + ((Subscript[B, 3] + Subscript[C, 3] z)/z) HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {b - 3, Subscript[b, 2]}, z] /; Subscript[B, 1] == ((b - 1) (b - 2) (b - Subscript[b, 2] - 1))/ ((1 + Subscript[a, 1] - b) (1 + Subscript[a, 2] - b) (1 + Subscript[a, 3] - b)) && Subscript[C, 1] == ((b - 1) ((2 b - 3) (Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3]) - Subscript[a, 1] Subscript[a, 2] - Subscript[a, 1] Subscript[a, 3] - Subscript[a, 2] Subscript[a, 3] - 7 + 9 b - 3 b^2))/((1 + Subscript[a, 1] - b) (1 + Subscript[a, 2] - b) (1 + Subscript[a, 3] - b)) && Subscript[B, 2] == ((b - 1) (b - 2) (4 - 2 b + Subscript[b, 2]))/((1 + Subscript[a, 1] - b) (1 + Subscript[a, 2] - b) (1 + Subscript[a, 3] - b)) && Subscript[C, 2] == ((b - 1) (b - 2) (3 b - 6 - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3]))/((1 + Subscript[a, 1] - b) (1 + Subscript[a, 2] - b) (1 + Subscript[a, 3] - b)) && Subscript[B, 3] == ((b - 1) (b - 2) (b - 3))/((1 + Subscript[a, 1] - b) (1 + Subscript[a, 2] - b) (1 + Subscript[a, 3] - b)) && Subscript[C, 3] == -(((b - 1) (b - 2) (b - 3))/((1 + Subscript[a, 1] - b) (1 + Subscript[a, 2] - b) (1 + Subscript[a, 3] - b)))

 Standard Form

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 MathML Form

 3 F 2 ( a 1 , a 2 , a 3 ; b , 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["b", 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] B 1 + C 1 z z 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[RowBox[List["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] + B 2 + C 2 z z 3 F 2 ( a 1 , a 2 , a 3 ; b - 2 , 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[RowBox[List["b", "-", "2"]], 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] + B 3 + C 3 z z 3 F 2 ( a 1 , a 2 , a 3 ; b - 3 , 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[RowBox[List["b", "-", "3"]], 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] /; B 1 ( b - 1 ) ( b - 2 ) ( b - b 2 - 1 ) ( 1 - b + a 1 ) ( 1 - b + a 2 ) ( 1 - b + a 3 ) C 1 ( ( b - 1 ) ( ( 2 b - 3 ) ( a 1 + a 2 + a 3 ) - 3 b 2 + 9 b - a 1 a 2 - a 1 a 3 - a 2 a 3 - 7 ) ) / ( ( 1 - b + a 1 ) ( 1 - b + a 2 ) ( 1 - b + a 3 ) ) B 2 ( b - 1 ) ( b - 2 ) ( b 2 - 2 b + 4 ) ( 1 - b + a 1 ) ( 1 - b + a 2 ) ( 1 - b + a 3 ) C 2 ( b - 1 ) ( b - 2 ) ( 3 b - a 1 - a 2 - a 3 - 6 ) ( 1 - b + a 1 ) ( 1 - b + a 2 ) ( 1 - b + a 3 ) B 3 ( b - 1 ) ( b - 2 ) ( b - 3 ) ( 1 - b + a 1 ) ( 1 - b + a 2 ) ( 1 - b + a 3 ) C 3 - ( b - 1 ) ( b - 2 ) ( b - 3 ) ( 1 - b + a 1 ) ( 1 - b + a 2 ) ( 1 - b + a 3 ) Condition HypergeometricPFQ Subscript a 1 Subscript a 2 Subscript a 3 b Subscript b 2 z Subscript B 1 Subscript C 1 z z -1 HypergeometricPFQ Subscript a 1 Subscript a 2 Subscript a 3 b -1 Subscript b 2 z Subscript B 2 Subscript C 2 z z -1 HypergeometricPFQ Subscript a 1 Subscript a 2 Subscript a 3 b -2 Subscript b 2 z Subscript B 3 Subscript C 3 z z -1 HypergeometricPFQ Subscript a 1 Subscript a 2 Subscript a 3 b -3 Subscript b 2 z Subscript B 1 b -1 b -2 b -1 Subscript b 2 -1 1 -1 b Subscript a 1 1 -1 b Subscript a 2 1 -1 b Subscript a 3 -1 Subscript C 1 b -1 2 b -3 Subscript a 1 Subscript a 2 Subscript a 3 -1 3 b 2 9 b -1 Subscript a 1 Subscript a 2 -1 Subscript a 1 Subscript a 3 -1 Subscript a 2 Subscript a 3 -7 1 -1 b Subscript a 1 1 -1 b Subscript a 2 1 -1 b Subscript a 3 -1 Subscript B 2 b -1 b -2 Subscript b 2 -1 2 b 4 1 -1 b Subscript a 1 1 -1 b Subscript a 2 1 -1 b Subscript a 3 -1 Subscript C 2 b -1 b -2 3 b -1 Subscript a 1 -1 Subscript a 2 -1 Subscript a 3 -6 1 -1 b Subscript a 1 1 -1 b Subscript a 2 1 -1 b Subscript a 3 -1 Subscript B 3 b -1 b -2 b -3 1 -1 b Subscript a 1 1 -1 b Subscript a 2 1 -1 b Subscript a 3 -1 Subscript C 3 -1 b -1 b -2 b -3 1 -1 b Subscript a 1 1 -1 b Subscript a 2 1 -1 b Subscript a 3 -1 [/itex]

 Rule Form

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

 2001-10-29