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/07.28.06.0028.01

 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[a, 2] - Subscript[a, 1]] Gamma[Subscript[a, 3] - Subscript[a, 1]] Gamma[Subscript[a, 4] - Subscript[a, 1]] Product[Gamma[Subscript[b, k]], {k, 1, 3}])/(Gamma[Subscript[a, 2]] Gamma[Subscript[a, 3]] Gamma[Subscript[a, 4]] Product[Gamma[Subscript[b, j] - Subscript[a, 1]], {j, 1, 3}])) Sum[(Pochhammer[Subscript[a, 1], j]/((-Subscript[z, 0])^j j!)) HypergeometricPFQ[{Subscript[a, 1] - Subscript[b, 1] + 1, Subscript[a, 1] - Subscript[b, 2] + 1, Subscript[a, 1] - Subscript[b, 3] + 1, Subscript[a, 1] + j}, {Subscript[a, 1] - Subscript[a, 2] + 1, Subscript[a, 1] - Subscript[a, 3] + 1, Subscript[a, 1] - Subscript[a, 4] + 1}, 1/Subscript[z, 0]] (z - Subscript[z, 0])^j, {j, 0, Infinity}])/ ((-(1/Subscript[z, 0]))^(Subscript[a, 1] Floor[Arg[-z + Subscript[z, 0]]/ (2 Pi)]) (-Subscript[z, 0])^(Subscript[a, 1] (1 + Floor[Arg[-z + Subscript[z, 0]]/(2 Pi)]))) + (((Gamma[Subscript[a, 1] - Subscript[a, 2]] Gamma[Subscript[a, 3] - Subscript[a, 2]] Gamma[Subscript[a, 4] - Subscript[a, 2]] Product[Gamma[Subscript[b, k]], {k, 1, 3}])/(Gamma[Subscript[a, 1]] Gamma[Subscript[a, 3]] Gamma[Subscript[a, 4]] Product[Gamma[Subscript[b, j] - Subscript[a, 2]], {j, 1, 3}])) Sum[(Pochhammer[Subscript[a, 2], j]/((-Subscript[z, 0])^j j!)) HypergeometricPFQ[{Subscript[a, 2] - Subscript[b, 1] + 1, Subscript[a, 2] - Subscript[b, 2] + 1, Subscript[a, 2] - Subscript[b, 3] + 1, Subscript[a, 2] + j}, {Subscript[a, 2] - Subscript[a, 1] + 1, Subscript[a, 2] - Subscript[a, 3] + 1, Subscript[a, 2] - Subscript[a, 4] + 1}, 1/Subscript[z, 0]] (z - Subscript[z, 0])^j, {j, 0, Infinity}])/ ((-(1/Subscript[z, 0]))^(Subscript[a, 2] Floor[Arg[-z + Subscript[z, 0]]/ (2 Pi)]) (-Subscript[z, 0])^(Subscript[a, 2] (1 + Floor[Arg[-z + Subscript[z, 0]]/(2 Pi)]))) + (((Gamma[Subscript[a, 1] - Subscript[a, 3]] Gamma[Subscript[a, 2] - Subscript[a, 3]] Gamma[Subscript[a, 4] - Subscript[a, 3]] Product[Gamma[Subscript[b, k]], {k, 1, 3}])/(Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]] Gamma[Subscript[a, 4]] Product[Gamma[Subscript[b, j] - Subscript[a, 3]], {j, 1, 3}])) Sum[(Pochhammer[Subscript[a, 3], j]/((-Subscript[z, 0])^j j!)) HypergeometricPFQ[{Subscript[a, 3] - Subscript[b, 1] + 1, Subscript[a, 3] - Subscript[b, 2] + 1, Subscript[a, 3] - Subscript[b, 3] + 1, Subscript[a, 3] + j}, {Subscript[a, 3] - Subscript[a, 1] + 1, Subscript[a, 3] - Subscript[a, 2] + 1, Subscript[a, 3] - Subscript[a, 4] + 1}, 1/Subscript[z, 0]] (z - Subscript[z, 0])^j, {j, 0, Infinity}])/ ((-(1/Subscript[z, 0]))^(Subscript[a, 3] Floor[Arg[-z + Subscript[z, 0]]/ (2 Pi)]) (-Subscript[z, 0])^(Subscript[a, 3] (1 + Floor[Arg[-z + Subscript[z, 0]]/(2 Pi)]))) + (((Gamma[Subscript[a, 1] - Subscript[a, 4]] Gamma[Subscript[a, 2] - Subscript[a, 4]] Gamma[Subscript[a, 3] - Subscript[a, 4]] Product[Gamma[Subscript[b, k]], {k, 1, 3}])/(Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]] Gamma[Subscript[a, 3]] Product[Gamma[Subscript[b, j] - Subscript[a, 4]], {j, 1, 3}])) Sum[(Pochhammer[Subscript[a, 4], j]/((-Subscript[z, 0])^j j!)) HypergeometricPFQ[{Subscript[a, 4] - Subscript[b, 1] + 1, Subscript[a, 4] - Subscript[b, 2] + 1, Subscript[a, 4] - Subscript[b, 3] + 1, Subscript[a, 4] + j}, {Subscript[a, 4] - Subscript[a, 1] + 1, Subscript[a, 4] - Subscript[a, 2] + 1, Subscript[a, 4] - Subscript[a, 3] + 1}, 1/Subscript[z, 0]] (z - Subscript[z, 0])^j, {j, 0, Infinity}])/ ((-(1/Subscript[z, 0]))^(Subscript[a, 4] Floor[Arg[-z + Subscript[z, 0]]/ (2 Pi)]) (-Subscript[z, 0])^(Subscript[a, 4] (1 + Floor[Arg[-z + Subscript[z, 0]]/(2 Pi)]))) /; Abs[Subscript[z, 0]] > 1 && ForAll[{j, k}, Element[{j, k}, Integers] && j != k && 1 <= j <= 4 && 1 <= k <= 4, !Element[Subscript[a, j] - Subscript[a, k], 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 ( a 2 - a 1 ) Γ ( a 3 - a 1 ) Γ ( a 4 - a 1 ) k = 1 3 Γ ( b k ) Γ ( a 2 ) Γ ( a 3 ) Γ ( a 4 ) j = 1 3 Γ ( b j - a 1 ) ( - z 0 ) - a 1 ( arg ( z 0 - z ) 2 π + 1 ) ( - 1 z 0 ) - a 1 arg ( z 0 - z ) 2 π j = 0 ( a 1 ) j TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["a", "1"], ")"]], "j"], Pochhammer] ( - z 0 ) - j j ! 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02