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/07.28.06.0006.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] == ((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[b, 3]] Gamma[Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]])/(Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]] Gamma[Subscript[a, 3]] Gamma[Subscript[a, 4]])) (1 - z)^(Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3] - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3] - Subscript[a, 4]) (1 + Subscript[d, 1] (z - 1) + Subscript[d, 2] (z - 1)^2 + \[Ellipsis]) + (HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, 1] + ((Subscript[a, 1] Subscript[a, 2] Subscript[a, 3] Subscript[a, 4])/ (Subscript[b, 1] Subscript[b, 2] Subscript[b, 3])) HypergeometricPFQ[{1 + Subscript[a, 1], 1 + Subscript[a, 2], 1 + Subscript[a, 3], 1 + Subscript[a, 4]}, {1 + Subscript[b, 1], 1 + Subscript[b, 2], 1 + Subscript[b, 3]}, 1] (z - 1) + ((Subscript[a, 1] (1 + Subscript[a, 1]) Subscript[a, 2] (1 + Subscript[a, 2]) Subscript[a, 3] (1 + Subscript[a, 3]) Subscript[a, 4] (1 + Subscript[a, 4]))/(2 Subscript[b, 1] (1 + Subscript[b, 1]) Subscript[b, 2] (1 + Subscript[b, 2]) Subscript[b, 3] (1 + Subscript[b, 3]))) HypergeometricPFQ[ {2 + Subscript[a, 1], 2 + Subscript[a, 2], 2 + Subscript[a, 3], 2 + Subscript[a, 4]}, {2 + Subscript[b, 1], 2 + Subscript[b, 2], 2 + Subscript[b, 3]}, 1] (z - 1)^2 + \[Ellipsis]) /; Abs[z - 1] < 1 && Subscript[d, 1] == (Subscript[a, 3] Subscript[a, 4] - Subscript[a, 3] Subscript[b, 1] - Subscript[a, 4] Subscript[b, 1] + Subscript[b, 1]^2 - Subscript[a, 3] Subscript[b, 2] - Subscript[a, 4] Subscript[b, 2] + Subscript[b, 1] Subscript[b, 2] + Subscript[b, 2]^2 + Subscript[a, 2] (Subscript[a, 3] + Subscript[a, 4] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]) + Subscript[a, 1] (Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]) - Subscript[a, 3] Subscript[b, 3] - Subscript[a, 4] Subscript[b, 3] + Subscript[b, 1] Subscript[b, 3] + Subscript[b, 2] Subscript[b, 3] + Subscript[b, 3]^2)/(-1 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]) && Subscript[d, 2] == ((Subscript[a, 1] + Subscript[a, 2] - Subscript[b, 1] - Subscript[b, 2]) (Subscript[a, 1] + Subscript[a, 3] - Subscript[b, 1] - Subscript[b, 2]) (Subscript[a, 2] + Subscript[a, 3] - Subscript[b, 1] - Subscript[b, 2]) + ((-Subscript[a, 3]) Subscript[b, 1] + Subscript[b, 1]^2 + Subscript[a, 2] (Subscript[a, 3] - Subscript[b, 1] - Subscript[b, 2]) + Subscript[a, 1] (Subscript[a, 2] + Subscript[a, 3] - Subscript[b, 1] - Subscript[b, 2]) - Subscript[a, 3] Subscript[b, 2] + Subscript[b, 1] Subscript[b, 2] + Subscript[b, 2]^2) (1 - 2 Subscript[a, 3] + 3 Subscript[b, 1] - Subscript[a, 3] Subscript[b, 1] + Subscript[b, 1]^2 + Subscript[a, 2] (-2 + Subscript[a, 3] - Subscript[b, 1] - Subscript[b, 2]) + Subscript[a, 1] (-2 + Subscript[a, 2] + Subscript[a, 3] - Subscript[b, 1] - Subscript[b, 2]) + 3 Subscript[b, 2] - Subscript[a, 3] Subscript[b, 2] + Subscript[b, 1] Subscript[b, 2] + Subscript[b, 2]^2))/(2 (-2 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]) (-1 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3])) && !Element[Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3] - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3] - Subscript[a, 4], Integers]

 Standard Form

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 MathML Form

 4 F 3 ( a 1 , a 2 , a 3 , a 4 ; b 1 , b 2 , b 3 ; 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[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], 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[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] Γ ( b 1 ) Γ ( b 2 ) Γ ( b 3 ) Γ ( a 1 + a 2 + a 3 + a 4 - b 1 - b 2 - b 3 ) Γ ( a 1 ) Γ ( a 2 ) Γ ( a 3 ) Γ ( a 4 ) ( 1 - z ) b 1 + b 2 + b 3 - a 1 - a 2 - a 3 - a 4 ( 1 + d 1 ( z - 1 ) + d 2 ( z - 1 ) 2 + ) + ( 4 F 3 ( a 1 , a 2 , a 3 , a 4 ; b 1 , b 2 , b 3 ; 1 ) 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[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], 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[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["1", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] + a 1 a 2 a 3 a 4 b 1 b 2 b 3 4 F 3 ( a 1 + 1 , a 2 + 1 , a 3 + 1 , a 4 + 1 ; 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 Date Added to functions.wolfram.com (modification date)

 2001-10-29