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/07.25.06.0008.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2]}, z] \[Proportional] ((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]])/(Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]])) z^\[Chi] E^z Sum[Subscript[c, k]/z^k, {k, 0, Infinity}] + (((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[a, 2] - Subscript[a, 1]])/(Gamma[Subscript[a, 2]] Gamma[Subscript[b, 1] - Subscript[a, 1]] Gamma[Subscript[b, 2] - Subscript[a, 1]])) HypergeometricPFQ[{Subscript[a, 1], 1 + Subscript[a, 1] - Subscript[b, 1], 1 + Subscript[a, 1] - Subscript[b, 2]}, {1 + Subscript[a, 1] - Subscript[a, 2]}, -(1/z)])/ (-z)^Subscript[a, 1] + (((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[a, 1] - Subscript[a, 2]])/(Gamma[Subscript[a, 1]] Gamma[Subscript[b, 1] - Subscript[a, 2]] Gamma[Subscript[b, 2] - Subscript[a, 2]])) HypergeometricPFQ[{Subscript[a, 2], 1 + Subscript[a, 2] - Subscript[b, 1], 1 + Subscript[a, 2] - Subscript[b, 2]}, {1 + Subscript[a, 2] - Subscript[a, 1]}, -(1/z)])/ (-z)^Subscript[a, 2] /; (Abs[z] -> Infinity) && \[Chi] == Subscript[a, 1] + Subscript[a, 2] - Subscript[b, 1] - Subscript[b, 2] && Subscript[c, 0] == 1 && Subscript[c, 1] == (Subscript[A, 2] - 1) \[Chi] + Subscript[b, 1] Subscript[b, 2] - Subscript[a, 1] Subscript[a, 2] && Subscript[c, k] == (1/k) ((1 - Subscript[B, 2] + 2 Subscript[a, 1] + Subscript[a, 1]^2 + 2 Subscript[a, 2] + Subscript[a, 2]^2 - Subscript[A, 2] Subscript[B, 2] + Subscript[a, 1] Subscript[a, 2] + Subscript[b, 1] Subscript[b, 2] + (2 Subscript[B, 2] - 3 (Subscript[A, 2] + 1)) k + 2 k^2) Subscript[c, k - 1] - (k - Subscript[A, 2] + Subscript[b, 1] - 1) (k - Subscript[A, 2] + Subscript[b, 2] - 1) (k - \[Chi] - 2) Subscript[c, k - 2]) && Subscript[A, 2] == Subscript[a, 1] + Subscript[a, 2] && Subscript[B, 2] == Subscript[b, 1] + Subscript[b, 2] && !Element[Subscript[a, 1] - Subscript[a, 2], Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"]]], "}"]], ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["b", "1"], "]"]], RowBox[List["Gamma", "[", SubscriptBox["b", "2"], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["a", "1"], "]"]], RowBox[List["Gamma", "[", SubscriptBox["a", "2"], "]"]]]]], SuperscriptBox["z", "\[Chi]"], SuperscriptBox["\[ExponentialE]", "z"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SubscriptBox["c", "k"], SuperscriptBox["z", RowBox[List["-", "k"]]]]]]]]], "+", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["b", "1"], "]"]], RowBox[List["Gamma", "[", SubscriptBox["b", "2"], "]"]], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["a", "1"]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["a", "2"], "]"]], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["a", "1"]]], "]"]], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["b", "2"], "-", SubscriptBox["a", "1"]]], "]"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", SubscriptBox["a", "1"]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["a", "2"]]], "}"]], ",", RowBox[List["-", FractionBox["1", "z"]]]]], "]"]]]], "+", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["b", "1"], "]"]], RowBox[List["Gamma", "[", SubscriptBox["b", "2"], "]"]], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["a", "2"]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["a", "1"], "]"]], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["a", "2"]]], "]"]], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["b", "2"], "-", SubscriptBox["a", "2"]]], "]"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", SubscriptBox["a", "2"]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "2"], ",", RowBox[List["1", "+", SubscriptBox["a", "2"], "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "2"], "-", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", SubscriptBox["a", "2"], "-", SubscriptBox["a", "1"]]], "}"]], ",", RowBox[List["-", FractionBox["1", "z"]]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "\[And]", RowBox[List["\[Chi]", "\[Equal]", RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["a", "2"], "-", SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]]]], "\[And]", RowBox[List[SubscriptBox["c", "0"], "\[Equal]", "1"]], "\[And]", RowBox[List[SubscriptBox["c", "1"], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["A", "2"], "-", "1"]], ")"]], "\[Chi]"]], "+", RowBox[List[SubscriptBox["b", "1"], SubscriptBox["b", "2"]]], "-", RowBox[List[SubscriptBox["a", "1"], SubscriptBox["a", "2"]]]]]]], "\[And]", RowBox[List[SubscriptBox["c", "k"], "\[Equal]", RowBox[List[FractionBox["1", "k"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SubscriptBox["B", "2"], "+", RowBox[List["2", " ", SubscriptBox["a", "1"]]], "+", SubsuperscriptBox["a", "1", "2"], "+", RowBox[List["2", " ", SubscriptBox["a", "2"]]], "+", SubsuperscriptBox["a", "2", "2"], "-", RowBox[List[SubscriptBox["A", "2"], SubscriptBox["B", "2"]]], "+", RowBox[List[SubscriptBox["a", "1"], SubscriptBox["a", "2"]]], "+", RowBox[List[SubscriptBox["b", "1"], SubscriptBox["b", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", SubscriptBox["B", "2"]]], "-", RowBox[List["3", " ", RowBox[List["(", RowBox[List[SubscriptBox["A", "2"], "+", "1"]], ")"]]]]]], ")"]], " ", "k"]], "+", RowBox[List["2", " ", SuperscriptBox["k", "2"]]]]], ")"]], " ", SubscriptBox["c", RowBox[List["k", "-", "1"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["k", "-", SubscriptBox["A", "2"], "+", SubscriptBox["b", "1"], "-", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["k", "-", SubscriptBox["A", "2"], "+", SubscriptBox["b", "2"], "-", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["k", "-", "\[Chi]", "-", "2"]], ")"]], " ", SubscriptBox["c", RowBox[List["k", "-", "2"]]]]]]], ")"]]]]]], "\[And]", RowBox[List[SubscriptBox["A", "2"], "\[Equal]", RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["a", "2"]]]]], "\[And]", RowBox[List[SubscriptBox["B", "2"], "\[Equal]", RowBox[List[SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"]]]]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List[RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["a", "2"]]], ",", "Integers"]], "]"]], "]"]]]]]]]]

 MathML Form

 2 F 2 ( a 1 , a 2 ; b 1 , b 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", 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]]]], 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] Γ ( b 1 ) Γ ( b 2 ) Γ ( a 1 ) Γ ( a 2 ) z z χ k = 0 c k z - k + Γ ( b 1 ) Γ ( b 2 ) Γ ( a 2 - a 1 ) Γ ( a 2 ) Γ ( b 1 - a 1 ) Γ ( b 2 - a 1 ) ( - z ) - a 1 3 F 1 ( a 1 , a 1 - b 1 + 1 , a 1 - b 2 + 1 ; a 1 - a 2 + 1 ; - 1 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["b", "1"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["a", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", "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 ( a 1 - a 2 ) Γ ( a 1 ) Γ ( b 1 - a 2 ) Γ ( b 2 - a 2 ) ( - z ) - a 2 3 F 1 ( a 2 , a 2 - b 1 + 1 , a 2 - b 2 + 1 ; - a 1 + a 2 + 1 ; - 1 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["b", "1"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], "+", SubscriptBox["a", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", "z"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) χ a 1 + a 2 - b 1 - b 2 c 0 1 c 1 ( A 2 - 1 ) χ + b 1 b 2 - a 1 a 2 c k 1 k ( ( 1 - B 2 + 2 a 1 + a 1 2 + 2 a 2 + a 2 2 - A 2 B 2 + a 1 a 2 + b 1 b 2 + ( 2 B 2 - 3 ( A 2 + 1 ) ) k + 2 k 2 ) c k - 1 - ( k - A 2 + b 1 - 1 ) ( k - A 2 + b 2 - 1 ) ( k - χ - 2 ) c k - 2 ) A 2 a 1 + a 2 B 2 b 1 + b 2 a 1 - a 2 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition Proportional HypergeometricPFQ Subscript a 1 Subscript a 2 Subscript b 1 Subscript b 2 z Gamma Subscript b 1 Gamma Subscript b 2 Gamma Subscript a 1 Gamma Subscript a 2 -1 z z χ k 0 Subscript c k z -1 k Gamma Subscript b 1 Gamma Subscript b 2 Gamma Subscript a 2 -1 Subscript a 1 Gamma Subscript a 2 Gamma Subscript b 1 -1 Subscript a 1 Gamma Subscript b 2 -1 Subscript a 1 -1 -1 z -1 Subscript a 1 HypergeometricPFQ Subscript a 1 Subscript a 1 -1 Subscript b 1 1 Subscript a 1 -1 Subscript b 2 1 Subscript a 1 -1 Subscript a 2 1 -1 1 z -1 Gamma Subscript b 1 Gamma Subscript b 2 Gamma Subscript a 1 -1 Subscript a 2 Gamma Subscript a 1 Gamma Subscript b 1 -1 Subscript a 2 Gamma Subscript b 2 -1 Subscript a 2 -1 -1 z -1 Subscript a 2 HypergeometricPFQ Subscript a 2 Subscript a 2 -1 Subscript b 1 1 Subscript a 2 -1 Subscript b 2 1 -1 Subscript a 1 Subscript a 2 1 -1 1 z -1 Rule z χ Subscript a 1 Subscript a 2 -1 Subscript b 1 -1 Subscript b 2 Subscript c 0 1 Subscript c 1 Subscript A 2 -1 χ Subscript b 1 Subscript b 2 -1 Subscript a 1 Subscript a 2 Subscript c k 1 k -1 1 -1 Subscript B 2 2 Subscript a 1 Subscript a 1 2 2 Subscript a 2 Subscript a 2 2 -1 Subscript A 2 Subscript B 2 Subscript a 1 Subscript a 2 Subscript b 1 Subscript b 2 2 Subscript B 2 -1 3 Subscript A 2 1 k 2 k 2 Subscript c k -1 -1 k -1 Subscript A 2 Subscript b 1 -1 k -1 Subscript A 2 Subscript b 2 -1 k -1 χ -2 Subscript c k -2 Subscript A 2 Subscript a 1 Subscript a 2 Subscript B 2 Subscript b 1 Subscript b 2 Subscript a 1 -1 Subscript a 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", SubscriptBox["a_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["bb", "1"], "]"]], " ", RowBox[List["Gamma", "[", SubscriptBox["bb", "2"], "]"]]]], ")"]], " ", SuperscriptBox["z", "\[Chi]"], " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SubscriptBox["c", "k"], " ", SuperscriptBox["z", RowBox[List["-", "k"]]]]]]]]], RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["aa", "1"], "]"]], " ", RowBox[List["Gamma", "[", SubscriptBox["aa", "2"], "]"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["bb", "1"], "]"]], " ", RowBox[List["Gamma", "[", SubscriptBox["bb", "2"], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["aa", "2"], "-", SubscriptBox["aa", "1"]]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", SubscriptBox["aa", "1"]]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["aa", "1"], ",", RowBox[List["1", "+", SubscriptBox["aa", "1"], "-", SubscriptBox["bb", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["aa", "1"], "-", SubscriptBox["bb", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", SubscriptBox["aa", "1"], "-", SubscriptBox["aa", "2"]]], "}"]], ",", RowBox[List["-", FractionBox["1", "z"]]]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["aa", "2"], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["bb", "1"], "-", SubscriptBox["aa", "1"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["bb", "2"], "-", SubscriptBox["aa", "1"]]], "]"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["bb", "1"], "]"]], " ", RowBox[List["Gamma", "[", SubscriptBox["bb", "2"], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["aa", "1"], "-", SubscriptBox["aa", "2"]]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", SubscriptBox["aa", "2"]]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["aa", "2"], ",", RowBox[List["1", "+", SubscriptBox["aa", "2"], "-", SubscriptBox["bb", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["aa", "2"], "-", SubscriptBox["bb", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", SubscriptBox["aa", "2"], "-", SubscriptBox["aa", "1"]]], "}"]], ",", RowBox[List["-", FractionBox["1", "z"]]]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["aa", "1"], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["bb", "1"], "-", SubscriptBox["aa", "2"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["bb", "2"], "-", SubscriptBox["aa", "2"]]], "]"]]]]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "&&", RowBox[List["\[Chi]", "\[Equal]", RowBox[List[SubscriptBox["aa", "1"], "+", SubscriptBox["aa", "2"], "-", SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "2"]]]]], "&&", RowBox[List[SubscriptBox["c", "0"], "\[Equal]", "1"]], "&&", RowBox[List[SubscriptBox["c", "1"], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["A", "2"], "-", "1"]], ")"]], " ", "\[Chi]"]], "+", RowBox[List[SubscriptBox["bb", "1"], " ", SubscriptBox["bb", "2"]]], "-", RowBox[List[SubscriptBox["aa", "1"], " ", SubscriptBox["aa", "2"]]]]]]], "&&", RowBox[List[SubscriptBox["c", "k"], "\[Equal]", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SubscriptBox["B", "2"], "+", RowBox[List["2", " ", SubscriptBox["aa", "1"]]], "+", SubsuperscriptBox["aa", "1", "2"], "+", RowBox[List["2", " ", SubscriptBox["aa", "2"]]], "+", SubsuperscriptBox["aa", "2", "2"], "-", RowBox[List[SubscriptBox["A", "2"], " ", SubscriptBox["B", "2"]]], "+", RowBox[List[SubscriptBox["aa", "1"], " ", SubscriptBox["aa", "2"]]], "+", RowBox[List[SubscriptBox["bb", "1"], " ", SubscriptBox["bb", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", SubscriptBox["B", "2"]]], "-", RowBox[List["3", " ", RowBox[List["(", RowBox[List[SubscriptBox["A", "2"], "+", "1"]], ")"]]]]]], ")"]], " ", "k"]], "+", RowBox[List["2", " ", SuperscriptBox["k", "2"]]]]], ")"]], " ", SubscriptBox["c", RowBox[List["k", "-", "1"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["k", "-", SubscriptBox["A", "2"], "+", SubscriptBox["bb", "1"], "-", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["k", "-", SubscriptBox["A", "2"], "+", SubscriptBox["bb", "2"], "-", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["k", "-", "\[Chi]", "-", "2"]], ")"]], " ", SubscriptBox["c", RowBox[List["k", "-", "2"]]]]]]], "k"]]], "&&", RowBox[List[SubscriptBox["A", "2"], "\[Equal]", RowBox[List[SubscriptBox["aa", "1"], "+", SubscriptBox["aa", "2"]]]]], "&&", RowBox[List[SubscriptBox["B", "2"], "\[Equal]", RowBox[List[SubscriptBox["bb", "1"], "+", SubscriptBox["bb", "2"]]]]], "&&", RowBox[List["!", RowBox[List[RowBox[List[SubscriptBox["aa", "1"], "-", SubscriptBox["aa", "2"]]], "\[Element]", "Integers"]]]]]]]]]]]]

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

 2001-10-29