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/07.31.06.0006.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] == (Product[Gamma[Subscript[b, k]], {k, 1, q}]/Product[Gamma[Subscript[a, k]], {k, 1, q + 1}]) (Sum[Subscript[k, j] (1 - j)^j, {j, 0, Subscript[\[Psi], q] - 1}] + (1 - z)^Subscript[\[Psi], q] Sum[(Subscript[p, j] + Subscript[q, j] Log[1 - z]) (1 - z)^j, {j, 0, Infinity}]) /; Abs[1 - z] < 1 && Subscript[\[Psi], q] == Sum[Subscript[b, j], {j, 1, q}] - Sum[Subscript[a, j], {j, 1, q + 1}] && q > 1 && (Subscript[k, j] == (((-1)^j Gamma[Subscript[a, 1] + j] Gamma[Subscript[a, 2] + j])/j!) Sum[((Subscript[\[Psi], q] + k - j - 1)!/ (Gamma[Subscript[a, 1] + Subscript[\[Psi], q] + k] Gamma[Subscript[a, 2] + Subscript[\[Psi], q] + k])) HypergeometricPFQExpansionCoefficient[{Subscript[a, 1], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, k], {k, 0, Infinity}] /; Re[Subscript[a, 3]] > -j && \[Ellipsis] && Re[Subscript[a, p + 1]] > -j) && (Subscript[p, j] == (((-1)^Subscript[\[Psi], q] Pochhammer[Subscript[a, 1] + Subscript[\[Psi], q], j] Pochhammer[Subscript[a, 2] + Subscript[\[Psi], q], j])/(j! (Subscript[\[Psi], q] + j)!)) ((-1)^j j! Sum[((k - j - 1)!/(Pochhammer[Subscript[a, 1] + Subscript[\[Psi], q], k] Pochhammer[Subscript[a, 2] + Subscript[\[Psi], q], k])) HypergeometricPFQExpansionCoefficient[ {Subscript[a, 1], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, k], {k, j + 1, Infinity}] + Sum[(Pochhammer[-j, k]/(Pochhammer[Subscript[a, 1] + Subscript[\[Psi], q], k] Pochhammer[Subscript[a, 2] + Subscript[\[Psi], q], k])) HypergeometricPFQExpansionCoefficient[{Subscript[a, 1], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, k] (PolyGamma[j - k + 1] + PolyGamma[j + Subscript[\[Psi], q] + 1] - PolyGamma[Subscript[\[Psi], q] + Subscript[a, 1] + j] - PolyGamma[Subscript[\[Psi], q] + Subscript[a, 2] + j]), {k, 0, j}]) /; Re[Subscript[a, 3]] > -j - Subscript[\[Psi], q] && \[Ellipsis] && Re[Subscript[a, p + 1]] > -j - Subscript[\[Psi], q]) && Subscript[q, j] == (((-1)^(Subscript[\[Psi], q] - 1) Pochhammer[Subscript[a, 1] + Subscript[\[Psi], q], j] Pochhammer[Subscript[a, 2] + Subscript[\[Psi], q], j])/ (j! (Subscript[\[Psi], q] + j)!)) Sum[(Pochhammer[-j, k]/(Pochhammer[Subscript[a, 1] + Subscript[\[Psi], q], k] Pochhammer[Subscript[a, 2] + Subscript[\[Psi], q], k])) HypergeometricPFQExpansionCoefficient[{Subscript[a, 1], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, k], {k, 0, j}] && Element[Subscript[\[Psi], q], Integers] && Subscript[\[Psi], q] >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", RowBox[List["q", "+", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "q"], RowBox[List["Gamma", "[", SubscriptBox["b", "k"], "]"]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], RowBox[List["q", "+", "1"]]], RowBox[List["Gamma", "[", SubscriptBox["a", "k"], "]"]]]]], RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List[SubscriptBox["\[Psi]", "q"], "-", "1"]]], RowBox[List[SubscriptBox["k", "j"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "j"]], ")"]], "j"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], SubscriptBox["\[Psi]", "q"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["p", "j"], "+", RowBox[List[SubscriptBox["q", "j"], RowBox[List["Log", "[", RowBox[List["1", "-", "z"]], "]"]]]]]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], "j"]]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["1", "-", "z"]], "]"]], "<", "1"]], "\[And]", RowBox[List[SubscriptBox["\[Psi]", "q"], "\[Equal]", RowBox[List[RowBox[List[StyleBox[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "q"], Rule[LimitsPositioningTokens, List["\[Sum]", "\[Product]", "\[Intersection]", "\[Union]", "\[UnionPlus]", "\[Wedge]", "\[Vee]", "lim", "max", "min", "\[CirclePlus]", "\[CircleMinus]", "\[CircleTimes]", "\[CircleDot]"]]], SubscriptBox["b", "j"]]], "-", RowBox[List[StyleBox[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], RowBox[List["q", "+", "1"]]], Rule[LimitsPositioningTokens, List["\[Sum]", "\[Product]", "\[Intersection]", "\[Union]", "\[UnionPlus]", "\[Wedge]", "\[Vee]", "lim", "max", "min", "\[CirclePlus]", "\[CircleMinus]", "\[CircleTimes]", "\[CircleDot]"]]], SubscriptBox["a", "j"]]]]]]], "\[And]", RowBox[List["q", ">", "1"]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["k", "j"], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "1"], "+", "j"]], "]"]], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "2"], "+", "j"]], "]"]]]], RowBox[List["j", "!"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["\[Psi]", "q"], "+", "k", "-", "j", "-", "1"]], ")"]], "!"]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["\[Psi]", "q"], "+", "k"]], "]"]], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "2"], "+", SubscriptBox["\[Psi]", "q"], "+", "k"]], "]"]]]]], RowBox[List["HypergeometricPFQExpansionCoefficient", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", RowBox[List["q", "+", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "k"]], "]"]]]]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", SubscriptBox["a", "3"], "]"]], ">", RowBox[List["-", "j"]]]], "\[And]", "\[Ellipsis]", "\[And]", RowBox[List[RowBox[List["Re", "[", SubscriptBox["a", RowBox[List["p", "+", "1"]]], "]"]], ">", RowBox[List["-", "j"]]]]]]]], ")"]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["p", "j"], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], SubscriptBox["\[Psi]", "q"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["\[Psi]", "q"]]], ",", "j"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[SubscriptBox["a", "2"], "+", SubscriptBox["\[Psi]", "q"]]], ",", "j"]], "]"]]]], RowBox[List[RowBox[List["j", "!"]], RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["\[Psi]", "q"], "+", "j"]], ")"]], "!"]]]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], RowBox[List["j", "!"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["j", "+", "1"]]]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["k", "-", "j", "-", "1"]], ")"]], "!"]], RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["\[Psi]", "q"]]], ",", "k"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[SubscriptBox["a", "2"], "+", SubscriptBox["\[Psi]", "q"]]], ",", "k"]], "]"]]]]], RowBox[List["HypergeometricPFQExpansionCoefficient", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", RowBox[List["q", "+", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "k"]], "]"]]]]]]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "j"], RowBox[List[FractionBox[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "j"]], ",", "k"]], "]"]], RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["\[Psi]", "q"]]], ",", "k"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[SubscriptBox["a", "2"], "+", SubscriptBox["\[Psi]", "q"]]], ",", "k"]], "]"]]]]], RowBox[List["HypergeometricPFQExpansionCoefficient", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", RowBox[List["q", "+", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "k"]], "]"]], RowBox[List["(", RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["j", "-", "k", "+", "1"]], "]"]], "+", RowBox[List["PolyGamma", "[", RowBox[List["j", "+", SubscriptBox["\[Psi]", "q"], "+", "1"]], "]"]], "-", RowBox[List["PolyGamma", "[", RowBox[List[SubscriptBox["\[Psi]", "q"], "+", SubscriptBox["a", "1"], "+", "j"]], "]"]], "-", RowBox[List["PolyGamma", "[", RowBox[List[SubscriptBox["\[Psi]", "q"], "+", SubscriptBox["a", "2"], "+", "j"]], "]"]]]], ")"]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", SubscriptBox["a", "3"], "]"]], ">", RowBox[List[RowBox[List["-", "j"]], "-", SubscriptBox["\[Psi]", "q"]]]]], "\[And]", "\[Ellipsis]", "\[And]", RowBox[List[RowBox[List["Re", "[", SubscriptBox["a", RowBox[List["p", "+", "1"]]], "]"]], ">", RowBox[List[RowBox[List["-", "j"]], "-", SubscriptBox["\[Psi]", "q"]]]]]]]]], ")"]], "\[And]", RowBox[List[SubscriptBox["q", "j"], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[SubscriptBox["\[Psi]", "q"], "-", "1"]]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["\[Psi]", "q"]]], ",", "j"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[SubscriptBox["a", "2"], "+", SubscriptBox["\[Psi]", "q"]]], ",", "j"]], "]"]]]], RowBox[List[RowBox[List["j", "!"]], RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["\[Psi]", "q"], "+", "j"]], ")"]], "!"]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "j"], RowBox[List[FractionBox[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "j"]], ",", "k"]], "]"]], RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["\[Psi]", "q"]]], ",", "k"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[SubscriptBox["a", "2"], "+", SubscriptBox["\[Psi]", "q"]]], ",", "k"]], "]"]]]]], RowBox[List["HypergeometricPFQExpansionCoefficient", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", RowBox[List["q", "+", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "k"]], "]"]]]]]]]]]], "\[And]", RowBox[List[SubscriptBox["\[Psi]", "q"], "\[Element]", "Integers"]], "\[And]", RowBox[List[SubscriptBox["\[Psi]", "q"], "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 q + 1 F q ( a 1 , , a q + 1 ; b 1 , , b q ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox[RowBox[List["q", "+", "1"]], TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", RowBox[List["q", "+", "1"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] k = 1 q Γ ( b k ) k = 1 q + 1 Γ ( a k ) ( j = 0 ψ q - 1 k j ( 1 - j ) j + ( 1 - z ) ψ q j = 0 ( p j + q j log ( 1 - z ) ) ( 1 - z ) j ) /; "\[LeftBracketingBar]" 1 - z "\[RightBracketingBar]" < 1 ψ q j = 1 q b j - j = 1 q + 1 a j q > 1 ( k j ( - 1 ) j Γ ( j + a 1 ) Γ ( j + a 2 ) j ! k = 0 ( k - j + ψ q - 1 ) ! k ( q ) ( { a 1 , , a q + 1 } , { b 1 , , b q } ) Γ ( k + a 1 + ψ q ) Γ ( k + a 2 + ψ q ) /; Re ( a 3 ) > - j Re ( a p + 1 ) > - j ) ( p j ( - 1 ) ψ q ( a 1 + ψ q ) j TagBox[SubscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["\[Psi]", "q"]]], ")"]], "j"], Pochhammer] ( a 2 + ψ q ) j TagBox[SubscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["a", "2"], "+", SubscriptBox["\[Psi]", "q"]]], ")"]], "j"], Pochhammer] j ! ( j + ψ q ) ! ( ( - 1 ) j j ! k = j + 1 ( k - j - 1 ) ! k ( q ) ( { a 1 , , a q + 1 } , { b 1 , , b q } ) ( a 1 + ψ q ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["\[Psi]", "q"]]], ")"]], "k"], Pochhammer] ( a 2 + ψ q ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["a", "2"], "+", SubscriptBox["\[Psi]", "q"]]], ")"]], "k"], Pochhammer] + k = 0 j ( - j ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", "j"]], ")"]], "k"], Pochhammer] k ( q ) ( { a 1 , , a q + 1 } , { b 1 , , b q } ) ( a 1 + ψ q ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["\[Psi]", "q"]]], ")"]], "k"], Pochhammer] ( a 2 + ψ q ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["a", "2"], "+", SubscriptBox["\[Psi]", "q"]]], ")"]], "k"], Pochhammer] ( ψ TagBox["\[Psi]", PolyGamma] ( j - k + 1 ) + ψ TagBox["\[Psi]", PolyGamma] ( j + ψ q + 1 ) - ψ TagBox["\[Psi]", PolyGamma] ( j + a 1 + ψ q ) - ψ TagBox["\[Psi]", PolyGamma] ( j + a 2 + ψ q ) ) ) /; Re ( a 3 ) > - j - ψ q Re ( a p + 1 ) > - j - ψ q ) q j ( - 1 ) ψ q - 1 ( a 1 + ψ q ) j TagBox[SubscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["\[Psi]", "q"]]], ")"]], "j"], Pochhammer] ( a 2 + ψ q ) j TagBox[SubscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["a", "2"], "+", SubscriptBox["\[Psi]", "q"]]], ")"]], "j"], Pochhammer] j ! ( j + ψ q ) ! k = 0 j ( - j ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", "j"]], ")"]], "k"], Pochhammer] k ( q ) ( { a 1 , , a q + 1 } , { b 1 , , b q } ) ( a 1 + ψ q ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["\[Psi]", "q"]]], ")"]], "k"], Pochhammer] ( a 2 + ψ q ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["a", "2"], "+", SubscriptBox["\[Psi]", "q"]]], ")"]], "k"], Pochhammer] ψ q Condition HypergeometricPFQ Subscript a 1 Subscript a q 1 Subscript b 1 Subscript b q z k 1 q Gamma Subscript b k k 1 q 1 Gamma Subscript a k -1 j 0 Subscript ψ q -1 Subscript k j 1 -1 j j 1 -1 z Subscript ψ q j 0 Subscript p j Subscript q j 1 -1 z 1 -1 z j 1 -1 z 1 Subscript ψ q j 1 q Subscript b j -1 j 1 q 1 Subscript a j q 1 Condition Subscript k j -1 j Gamma j Subscript a 1 Gamma j Subscript a 2 j -1 k 0 k -1 j Subscript ψ q -1 Subscript k q Subscript a 1 Subscript a q 1 Subscript b 1 Subscript b q Gamma k Subscript a 1 Subscript ψ q Gamma k Subscript a 2 Subscript ψ q -1 Subscript a 3 -1 j Subscript a p 1 -1 j Condition Subscript p j -1 Subscript ψ q Pochhammer Subscript a 1 Subscript ψ q j Pochhammer Subscript a 2 Subscript ψ q j j j Subscript ψ q -1 -1 j j k j 1 k -1 j -1 Subscript k q Subscript a 1 Subscript a q 1 Subscript b 1 Subscript b q Pochhammer Subscript a 1 Subscript ψ q k Pochhammer Subscript a 2 Subscript ψ q k -1 k 0 j Pochhammer -1 j k Subscript k q Subscript a 1 Subscript a q 1 Subscript b 1 Subscript b q Pochhammer Subscript a 1 Subscript ψ q k Pochhammer Subscript a 2 Subscript ψ q k -1 PolyGamma j -1 k 1 PolyGamma j Subscript ψ q 1 -1 PolyGamma j Subscript a 1 Subscript ψ q -1 PolyGamma j Subscript a 2 Subscript ψ q Subscript a 3 -1 j -1 Subscript ψ q Subscript a p 1 -1 j -1 Subscript ψ q Subscript q j -1 Subscript ψ q -1 Pochhammer Subscript a 1 Subscript ψ q j Pochhammer Subscript a 2 Subscript ψ q j j j Subscript ψ q -1 k 0 j Pochhammer -1 j k Subscript k q Subscript a 1 Subscript a q 1 Subscript b 1 Subscript b q Pochhammer Subscript a 1 Subscript ψ q k Pochhammer Subscript a 2 Subscript ψ q k -1 Subscript ψ q [/itex]

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

 2001-10-29