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/07.27.17.0001.01

 Input Form

 HypergeometricPFQ[{a, Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z] == (Subscript[B, 1] + Subscript[C, 1] z) HypergeometricPFQ[ {a + 1, Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z] + (Subscript[B, 2] + Subscript[C, 2] z) HypergeometricPFQ[{a + 2, Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z] + (Subscript[B, 3] + Subscript[C, 3] z) HypergeometricPFQ[ {a + 3, Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z] /; Subscript[B, 1] == ((1 + a) (4 + 3 a - 2 Subscript[b, 1] - 2 Subscript[b, 2]) + Subscript[b, 1] Subscript[b, 2])/ ((1 + a - Subscript[b, 1]) (1 + a - Subscript[b, 2])) && Subscript[C, 1] == ((Subscript[a, 2] - a - 1) (1 - Subscript[a, 3] + a))/ ((1 + a - Subscript[b, 1]) (1 + a - Subscript[b, 2])) && Subscript[B, 2] == ((1 + a) (Subscript[b, 1] + Subscript[b, 2] - 3 a - 5))/ ((1 + a - Subscript[b, 1]) (1 + a - Subscript[b, 2])) && Subscript[C, 2] == ((1 + a) (3 - Subscript[a, 2] - Subscript[a, 3] + 2 a))/ ((1 + a - Subscript[b, 1]) (1 + a - Subscript[b, 2])) && Subscript[B, 3] == ((1 + a) (2 + a))/((1 + a - Subscript[b, 1]) (1 + a - Subscript[b, 2])) && Subscript[C, 3] == -(((a + 1) (a + 2))/((1 + a - Subscript[b, 1]) (1 + a - Subscript[b, 2])))

 Standard Form

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 MathML Form

 3 F 2 ( a , 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["a", 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] ( B 1 + C 1 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[RowBox[List["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] + ( B 2 + C 2 z ) 3 F 2 ( a + 2 , 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[RowBox[List["a", "+", "2"]], 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] + ( B 3 + C 3 z ) 3 F 2 ( a + 3 , 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[RowBox[List["a", "+", "3"]], 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] /; B 1 b 1 b 2 + ( a + 1 ) ( 3 a - 2 b 1 - 2 b 2 + 4 ) ( a - b 1 + 1 ) ( a - b 2 + 1 ) C 1 ( - a + a 2 - 1 ) ( a - a 3 + 1 ) ( a - b 1 + 1 ) ( a - b 2 + 1 ) B 2 ( a + 1 ) ( - 3 a + b 1 + b 2 - 5 ) ( a - b 1 + 1 ) ( a - b 2 + 1 ) C 2 ( a + 1 ) ( 2 a - a 2 - a 3 + 3 ) ( a - b 1 + 1 ) ( a - b 2 + 1 ) B 3 ( a + 1 ) ( a + 2 ) ( a - b 1 + 1 ) ( a - b 2 + 1 ) C 3 - ( a + 1 ) ( a + 2 ) ( a - b 1 + 1 ) ( a - b 2 + 1 ) Condition HypergeometricPFQ a Subscript a 2 Subscript a 3 Subscript b 1 Subscript b 2 z Subscript B 1 Subscript C 1 z HypergeometricPFQ a 1 Subscript a 2 Subscript a 3 Subscript b 1 Subscript b 2 z Subscript B 2 Subscript C 2 z HypergeometricPFQ a 2 Subscript a 2 Subscript a 3 Subscript b 1 Subscript b 2 z Subscript B 3 Subscript C 3 z HypergeometricPFQ a 3 Subscript a 2 Subscript a 3 Subscript b 1 Subscript b 2 z Subscript B 1 Subscript b 1 Subscript b 2 a 1 3 a -1 2 Subscript b 1 -1 2 Subscript b 2 4 a -1 Subscript b 1 1 a -1 Subscript b 2 1 -1 Subscript C 1 -1 a Subscript a 2 -1 a -1 Subscript a 3 1 a -1 Subscript b 1 1 a -1 Subscript b 2 1 -1 Subscript B 2 a 1 -3 a Subscript b 1 Subscript b 2 -5 a -1 Subscript b 1 1 a -1 Subscript b 2 1 -1 Subscript C 2 a 1 2 a -1 Subscript a 2 -1 Subscript a 3 3 a -1 Subscript b 1 1 a -1 Subscript b 2 1 -1 Subscript B 3 a 1 a 2 a -1 Subscript b 1 1 a -1 Subscript b 2 1 -1 Subscript C 3 -1 a 1 a 2 a -1 Subscript b 1 1 a -1 Subscript b 2 1 -1 [/itex]

 Rule Form

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

 2001-10-29