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http://functions.wolfram.com/07.23.06.0060.01
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Hypergeometric2F1[a, a + n, c, z] == Subscript[F, Infinity][z, a, a + n,
c] /; (Subscript[F, n][z, a, a + n, c] ==
((Gamma[c] (-z)^(-a - n))/(Gamma[a + n] Gamma[c - a]))
Sum[(((Pochhammer[a, k + n] Pochhammer[1 + a - c, k + n])/
(k! (k + n)!)) (PolyGamma[k + n + 1] + PolyGamma[k + 1] -
PolyGamma[a + n + k] - PolyGamma[c - a - n - k] + Log[-z]))/z^k,
{k, 0, m}] + ((Gamma[c]/Gamma[a + n])
Sum[(Pochhammer[a, k] Gamma[n - k])/(k! Gamma[c - a - k])/z^k,
{k, 0, n - 1}])/(-z)^a == Hypergeometric2F1[a, a + n, c, z] -
(((-1)^n Gamma[c])/(Gamma[a] Gamma[a + n]))
MeijerG[{{-a - m - n, -a - m - n}, {1 - a, 1 - a - n}},
{{0, -a - n - m, -a - n - m}, {1 - c}}, -z] && Element[m, Integers] &&
m >= 0) && Element[n, Integers] && n >= 0 && !Element[c - a, Integers]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["a", ",", RowBox[List["a", "+", "n"]], ",", "c", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SubscriptBox["F", "\[Infinity]"], "[", RowBox[List["z", ",", "a", ",", RowBox[List["a", "+", "n"]], ",", "c"]], "]"]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["F", "n"], "[", RowBox[List["z", ",", "a", ",", RowBox[List["a", "+", "n"]], ",", "c"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", "c", "]"]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[RowBox[List["-", "a"]], "-", "n"]]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", "+", "n"]], "]"]], RowBox[List["Gamma", "[", RowBox[List["c", "-", "a"]], "]"]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "m"], RowBox[List[FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["a", ",", RowBox[List["k", "+", "n"]]]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "+", "a", "-", "c"]], ",", RowBox[List["k", "+", "n"]]]], "]"]]]], RowBox[List[RowBox[List["k", "!"]], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "n"]], ")"]], "!"]]]]], RowBox[List["(", RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["k", "+", "n", "+", "1"]], "]"]], "+", RowBox[List["PolyGamma", "[", RowBox[List["k", "+", "1"]], "]"]], "-", RowBox[List["PolyGamma", "[", RowBox[List["a", "+", "n", "+", "k"]], "]"]], "-", RowBox[List["PolyGamma", "[", RowBox[List["c", "-", "a", "-", "n", "-", "k"]], "]"]], "+", RowBox[List["Log", "[", RowBox[List["-", "z"]], "]"]]]], ")"]], SuperscriptBox["z", RowBox[List["-", "k"]]]]]]]]], "+", RowBox[List[FractionBox[RowBox[List["Gamma", "[", "c", "]"]], RowBox[List["Gamma", "[", RowBox[List["a", "+", "n"]], "]"]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "a"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "1"]]], RowBox[List[FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["a", ",", "k"]], "]"]], RowBox[List["Gamma", "[", RowBox[List["n", "-", "k"]], "]"]]]], RowBox[List[RowBox[List["k", "!"]], RowBox[List["Gamma", "[", RowBox[List["c", "-", "a", "-", "k"]], "]"]]]]], SuperscriptBox["z", RowBox[List["-", "k"]]]]]]]]]]], "\[Equal]", RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["a", ",", RowBox[List["a", "+", "n"]], ",", "c", ",", "z"]], "]"]], "-", " ", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], RowBox[List["Gamma", "[", "c", "]"]]]], RowBox[List[RowBox[List["Gamma", "[", "a", "]"]], RowBox[List["Gamma", "[", RowBox[List["a", "+", "n"]], "]"]]]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "-", "m", "-", "n"]], ",", RowBox[List[RowBox[List["-", "a"]], "-", "m", "-", "n"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "a"]], ",", RowBox[List["1", "-", "a", "-", "n"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List[RowBox[List["-", "a"]], "-", "n", "-", "m"]], ",", RowBox[List[RowBox[List["-", "a"]], "-", "n", "-", "m"]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", "c"]], "}"]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]]]]]]]], StyleBox[")", Rule[FontWeight, "Plain"]]]], "\[And]", RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", "\[GreaterEqual]", "0"]]]], ")"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List[RowBox[List["c", "-", "a"]], ",", "Integers"]], "]"]], "]"]]]]]]]]
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<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> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> </mrow> </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]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "+", "n"]], 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> <msub> <mi> F </mi> <mi> ∞ </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> a </mi> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> , </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> F </mi> <mi> n </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> a </mi> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> , </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> </msup> </mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mfrac> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", "a", ")"]], "k"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mi> k </mi> </mrow> </msup> </mrow> <mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> n </mi> </mrow> </msup> </mrow> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> m </mi> </munderover> <mrow> <mfrac> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mrow> <mi> k </mi> <mo> + </mo> <mi> n </mi> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", "a", ")"]], RowBox[List["k", "+", "n"]]], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> k </mi> <mo> + </mo> <mi> n </mi> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List["a", "-", "c", "+", "1"]], ")"]], RowBox[List["k", "+", "n"]]], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mrow> <mi> k </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mrow> <mi> k </mi> <mo> + </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mi> k </mi> <mo> - </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> k </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mi> k </mi> </mrow> </msup> </mrow> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <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> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> </mrow> </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]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "+", "n"]], 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> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <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> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> m </mi> <mo> - </mo> <mi> n </mi> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> m </mi> <mo> - </mo> <mi> n </mi> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> m </mi> <mo> - </mo> <mi> n </mi> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> m </mi> <mo> - </mo> <mi> n </mi> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> c </mi> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["4", ",", "4"]], RowBox[List["3", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["-", "z"]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List[RowBox[List["-", "a"]], "-", "m", "-", "n"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", "a"]], "-", "m", "-", "n"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "a"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", "a"]], "-", "n", "+", "1"]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", "a"]], "-", "m", "-", 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</apply> <apply> <apply> <ci> Subscript </ci> <ci> F </ci> <infinity /> </apply> <ci> z </ci> <ci> a </ci> <apply> <plus /> <ci> a </ci> <ci> n </ci> </apply> <ci> c </ci> </apply> </apply> <apply> <and /> <apply> <and /> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> F </ci> <ci> n </ci> </apply> <ci> z </ci> <ci> a </ci> <apply> <plus /> <ci> a </ci> <ci> n </ci> </apply> <ci> c </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <ci> Gamma </ci> <ci> c </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <ci> n </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> 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type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <ci> n </ci> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> m </ci> </uplimit> <apply> <times /> <apply> <times /> <apply> <ci> Pochhammer </ci> <ci> a </ci> <apply> <plus /> <ci> k </ci> <ci> n </ci> </apply> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> k </ci> <ci> n </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <ci> k </ci> </apply> <apply> <factorial /> <apply> <plus /> <ci> k </ci> <ci> n </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <ci> PolyGamma </ci> <apply> <plus /> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> PolyGamma </ci> <apply> <plus /> <ci> k </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> PolyGamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> PolyGamma </ci> <apply> <plus /> <ci> a </ci> <ci> k </ci> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> Hypergeometric2F1 </ci> <ci> a </ci> <apply> <plus /> <ci> a </ci> <ci> n </ci> </apply> <ci> c </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <ci> Gamma </ci> <ci> c </ci> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <ci> n </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 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Date Added to functions.wolfram.com (modification date)
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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] | |
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