|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.23.06.0055.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Hypergeometric2F1[a, b, c, z] \[Proportional]
Piecewise[{{ComplexInfinity, Element[-c, Integers] && -c >= 0 &&
((Element[-a, Integers] && -a >= 0 && c - a > 0) ||
(Element[-b, Integers] && -b >= 0 && c - b > 0))},
{(Gamma[c - a - b] Gamma[c])/(Gamma[c - a] Gamma[c - b]),
Re[c - a - b] > 0}, {((Gamma[a + b - c] Gamma[c])/(Gamma[a] Gamma[b]))
(1 - z)^(c - a - b), Re[c - a - b] < 0},
{-((Gamma[a + b] Log[1 - z])/(Gamma[a] Gamma[b])), c == a + b}},
(Gamma[c - a - b] Gamma[c])/(Gamma[c - a] Gamma[c - b]) +
((Gamma[a + b - c] Gamma[c])/(Gamma[a] Gamma[b])) (1 - z)^(c - a - b)] /;
(z -> 1)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["a", ",", "b", ",", "c", ",", "z"]], "]"]], "\[Proportional]", RowBox[List["Piecewise", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["ComplexInfinity", ",", RowBox[List[RowBox[List[RowBox[List["-", "c"]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["-", "c"]], "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["-", "a"]], "\[GreaterEqual]", "0"]], "\[And]", RowBox[List[RowBox[List["c", "-", "a"]], ">", "0"]]]], ")"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["-", "b"]], "\[GreaterEqual]", "0"]], "\[And]", RowBox[List[RowBox[List["c", "-", "b"]], ">", "0"]]]], ")"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["c", "-", "a", "-", "b"]], "]"]], RowBox[List["Gamma", "[", "c", "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["c", "-", "a"]], "]"]], RowBox[List["Gamma", "[", RowBox[List["c", "-", "b"]], "]"]]]]], " ", ",", RowBox[List[RowBox[List["Re", "[", RowBox[List["c", "-", "a", "-", "b"]], "]"]], ">", "0"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", "+", "b", "-", "c"]], "]"]], RowBox[List["Gamma", "[", "c", "]"]]]], RowBox[List[RowBox[List["Gamma", "[", "a", "]"]], " ", RowBox[List["Gamma", "[", "b", "]"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["c", "-", "a", "-", "b"]]]]], " ", ",", RowBox[List[RowBox[List["Re", "[", RowBox[List["c", "-", "a", "-", "b"]], "]"]], "<", "0"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", "+", "b"]], "]"]], RowBox[List["Log", "[", RowBox[List["1", "-", "z"]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", "a", "]"]], RowBox[List["Gamma", "[", "b", "]"]]]]]]], " ", ",", RowBox[List["c", "\[Equal]", RowBox[List["a", "+", "b"]]]]]], "}"]]]], "}"]], ",", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["c", "-", "a", "-", "b"]], "]"]], RowBox[List["Gamma", "[", "c", "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["c", "-", "a"]], "]"]], RowBox[List["Gamma", "[", RowBox[List["c", "-", "b"]], "]"]]]]], "+", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", "+", "b", "-", "c"]], "]"]], RowBox[List["Gamma", "[", "c", "]"]]]], RowBox[List[RowBox[List["Gamma", "[", "a", "]"]], " ", RowBox[List["Gamma", "[", "b", "]"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["c", "-", "a", "-", "b"]]]]]]]]], "]"]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "1"]], ")"]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ; </mo> <mi> c </mi> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", Hypergeometric2F1, Rule[Editable, True]], ",", TagBox["b", Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox["c", Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox["z", Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] </annotation> </semantics> <mo> ∝ </mo> <mrow> <mo>  </mo> <mtable> <mtr> <mtd> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> </mtd> <mtd> <mrow> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> ∈ </mo> <mi> ℕ </mi> </mrow> <mo> ∧ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> ∈ </mo> <mi> ℕ </mi> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> c </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> > </mo> <mn> 0 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ∨ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> ∈ </mo> <mi> ℕ </mi> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> c </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> > </mo> <mn> 0 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mtd> <mtd> <mrow> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> > </mo> <mn> 0 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> c </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msup> </mrow> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> </mtd> <mtd> <mrow> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> < </mo> <mn> 0 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <mi> c </mi> <mo>  </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> c </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msup> </mrow> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mtd> <mtd> <semantics> <mi> True </mi> <annotation encoding='Mathematica'> TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] </annotation> </semantics> </mtd> </mtr> </mtable> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> Hypergeometric2F1 </ci> <ci> a </ci> <ci> b </ci> <ci> c </ci> <ci> z </ci> </apply> <piecewise> <piece> <apply> <ci> OverTilde </ci> <infinity /> </apply> <apply> <and /> <apply> <in /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <ci> ℕ </ci> </apply> <apply> <or /> <apply> <and /> <apply> <in /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <ci> ℕ </ci> </apply> <apply> <gt /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <and /> <apply> <in /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> ℕ </ci> </apply> <apply> <gt /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </piece> <piece> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <ci> c </ci> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <gt /> <apply> <real /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </piece> <piece> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <ci> c </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <apply> <ci> Gamma </ci> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <lt /> <apply> <real /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </piece> <piece> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <apply> <ci> Gamma </ci> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <ci> c </ci> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> </apply> </piece> <otherwise> <apply> <plus /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <ci> c </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <apply> <ci> Gamma </ci> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <ci> c </ci> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </otherwise> </piecewise> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["a_", ",", "b_", ",", "c_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Piecewise]", GridBox[List[List["ComplexInfinity", RowBox[List[RowBox[List[RowBox[List["-", "c"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "c"]], "\[GreaterEqual]", "0"]], "&&", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "a"]], "\[GreaterEqual]", "0"]], "&&", RowBox[List[RowBox[List["c", "-", "a"]], ">", "0"]]]], ")"]], "||", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "b"]], "\[GreaterEqual]", "0"]], "&&", RowBox[List[RowBox[List["c", "-", "b"]], ">", "0"]]]], ")"]]]], ")"]]]]], List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["c", "-", "a", "-", "b"]], "]"]], " ", RowBox[List["Gamma", "[", "c", "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["c", "-", "a"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["c", "-", "b"]], "]"]]]]], RowBox[List[RowBox[List["Re", "[", RowBox[List["c", "-", "a", "-", "b"]], "]"]], ">", "0"]]], List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", "+", "b", "-", "c"]], "]"]], " ", RowBox[List["Gamma", "[", "c", "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["c", "-", "a", "-", "b"]]]]], RowBox[List[RowBox[List["Gamma", "[", "a", "]"]], " ", RowBox[List["Gamma", "[", "b", "]"]]]]], RowBox[List[RowBox[List["Re", "[", RowBox[List["c", "-", "a", "-", "b"]], "]"]], "<", "0"]]], List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", "+", "b"]], "]"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", "z"]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", "a", "]"]], " ", RowBox[List["Gamma", "[", "b", "]"]]]]]]], RowBox[List["c", "\[Equal]", RowBox[List["a", "+", "b"]]]]], List[RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["c", "-", "a", "-", "b"]], "]"]], " ", RowBox[List["Gamma", "[", "c", "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["c", "-", "a"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["c", "-", "b"]], "]"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", "+", "b", "-", "c"]], "]"]], " ", RowBox[List["Gamma", "[", "c", "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["c", "-", "a", "-", "b"]]]]], RowBox[List[RowBox[List["Gamma", "[", "a", "]"]], " ", RowBox[List["Gamma", "[", "b", "]"]]]]]]], TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "1"]], ")"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] | |
|
|
|