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/07.26.17.0001.01

 Input Form

 HypergeometricPFQ[{a, Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] == (Subscript[B, 1] + Subscript[C, 1] z) HypergeometricPFQ[{1 + a, Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] + (Subscript[B, 2] + Subscript[C, 2] z) HypergeometricPFQ[ {2 + a, Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] + Subscript[B, 3] HypergeometricPFQ[ {3 + a, Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] + Subscript[B, 4] HypergeometricPFQ[ {4 + a, Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] /; Subscript[B, 1] == ((1 + a) (8 + 11 a + 4 a^2 - (4 + 3 a) (Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3]) + 2 (Subscript[b, 1] Subscript[b, 2] + Subscript[b, 1] Subscript[b, 3] + Subscript[b, 2] Subscript[b, 3])) - Subscript[b, 1] Subscript[b, 2] Subscript[b, 3])/((1 + a - Subscript[b, 1]) (1 + a - Subscript[b, 2]) (1 + a - Subscript[b, 3])) && Subscript[C, 1] == -((1 + a - Subscript[a, 2])/((1 + a - Subscript[b, 1]) (1 + a - Subscript[b, 2]) (1 + a - Subscript[b, 3]))) && Subscript[B, 2] == -(((1 + a) (19 + 21 a + 6 a^2 - (5 + 3 a) (Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3]) + Subscript[b, 2] Subscript[b, 3] + Subscript[b, 1] Subscript[b, 2] + Subscript[b, 1] Subscript[b, 3]))/((1 + a - Subscript[b, 1]) (1 + a - Subscript[b, 2]) (1 + a - Subscript[b, 3]))) && Subscript[C, 2] == (1 + a)/((1 + a - Subscript[b, 1]) (1 + a - Subscript[b, 2]) (1 + a - Subscript[b, 3])) && Subscript[B, 3] == ((1 + a) (2 + a) (9 + 4 a - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]))/((1 + a - Subscript[b, 1]) (1 + a - Subscript[b, 2]) (1 + a - Subscript[b, 3])) && Subscript[B, 4] == -(((1 + a) (2 + a) (3 + a))/((1 + a - Subscript[b, 1]) (1 + a - Subscript[b, 2]) (1 + a - Subscript[b, 3])))

 Standard Form

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 MathML Form

 2 F 3 ( a , a 2 ; b 1 , b 2 , b 3 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], 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]], ",", TagBox[SubscriptBox["b", "3"], 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 ) 2 F 3 ( a + 1 , a 2 ; b 1 , b 2 , b 3 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", 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[SubscriptBox["a", "2"], 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]], ",", TagBox[SubscriptBox["b", "3"], 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 ) 2 F 3 ( a + 2 , a 2 ; b 1 , b 2 , b 3 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["3", 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]]]], 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]], ",", TagBox[SubscriptBox["b", "3"], 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 2 F 3 ( a + 3 , a 2 ; b 1 , b 2 , b 3 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["3", 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]]]], 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]], ",", TagBox[SubscriptBox["b", "3"], 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 4 2 F 3 ( a + 4 , a 2 ; b 1 , b 2 , b 3 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["a", "+", "4"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], 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]], ",", TagBox[SubscriptBox["b", "3"], 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 ( ( a + 1 ) ( 4 a 2 + 11 a - ( 3 a + 4 ) ( b 1 + b 2 + b 3 ) + 2 ( b 1 b 2 + b 3 b 2 + b 1 b 3 ) + 8 ) - b 1 b 2 b 3 ) / ( ( a - b 1 + 1 ) ( a - b 2 + 1 ) ( a - b 3 + 1 ) ) C 1 - a - a 2 + 1 ( a - b 1 + 1 ) ( a - b 2 + 1 ) ( a - b 3 + 1 ) B 2 - ( ( a + 1 ) ( 6 a 2 + 21 a + b 1 b 2 + b 1 b 3 + b 2 b 3 - ( 3 a + 5 ) ( b 1 + b 2 + b 3 ) + 19 ) ) / ( ( a - b 1 + 1 ) ( a - b 2 + 1 ) ( a - b 3 + 1 ) ) C 2 a + 1 ( a - b 1 + 1 ) ( a - b 2 + 1 ) ( a - b 3 + 1 ) B 3 ( a + 1 ) ( a + 2 ) ( 4 a - b 1 - b 2 - b 3 + 9 ) ( a - b 1 + 1 ) ( a - b 2 + 1 ) ( a - b 3 + 1 ) B 4 - ( a + 1 ) ( a + 2 ) ( a + 3 ) ( a - b 1 + 1 ) ( a - b 2 + 1 ) ( a - b 3 + 1 ) Condition HypergeometricPFQ a Subscript a 2 Subscript b 1 Subscript b 2 Subscript b 3 z Subscript B 1 Subscript C 1 z HypergeometricPFQ a 1 Subscript a 2 Subscript b 1 Subscript b 2 Subscript b 3 z Subscript B 2 Subscript C 2 z HypergeometricPFQ a 2 Subscript a 2 Subscript b 1 Subscript b 2 Subscript b 3 z Subscript B 3 HypergeometricPFQ a 3 Subscript a 2 Subscript b 1 Subscript b 2 Subscript b 3 z Subscript B 4 HypergeometricPFQ a 4 Subscript a 2 Subscript b 1 Subscript b 2 Subscript b 3 z Subscript B 1 a 1 4 a 2 11 a -1 3 a 4 Subscript b 1 Subscript b 2 Subscript b 3 2 Subscript b 1 Subscript b 2 Subscript b 3 Subscript b 2 Subscript b 1 Subscript b 3 8 -1 Subscript b 1 Subscript b 2 Subscript b 3 a -1 Subscript b 1 1 a -1 Subscript b 2 1 a -1 Subscript b 3 1 -1 Subscript C 1 -1 a -1 Subscript a 2 1 a -1 Subscript b 1 1 a -1 Subscript b 2 1 a -1 Subscript b 3 1 -1 Subscript B 2 -1 a 1 6 a 2 21 a Subscript b 1 Subscript b 2 Subscript b 1 Subscript b 3 Subscript b 2 Subscript b 3 -1 3 a 5 Subscript b 1 Subscript b 2 Subscript b 3 19 a -1 Subscript b 1 1 a -1 Subscript b 2 1 a -1 Subscript b 3 1 -1 Subscript C 2 a 1 a -1 Subscript b 1 1 a -1 Subscript b 2 1 a -1 Subscript b 3 1 -1 Subscript B 3 a 1 a 2 4 a -1 Subscript b 1 -1 Subscript b 2 -1 Subscript b 3 9 a -1 Subscript b 1 1 a -1 Subscript b 2 1 a -1 Subscript b 3 1 -1 Subscript B 4 -1 a 1 a 2 a 3 a -1 Subscript b 1 1 a -1 Subscript b 2 1 a -1 Subscript b 3 1 -1 [/itex]

 Rule Form

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

 2001-10-29