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http://functions.wolfram.com/06.10.20.0003.01
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D[Pochhammer[a, n], n] == Pochhammer[a, n] PolyGamma[a + n]
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Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "n"], RowBox[List["Pochhammer", "[", RowBox[List["a", ",", "n"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["a", ",", "n"]], "]"]], " ", RowBox[List["PolyGamma", "[", RowBox[List["a", "+", "n"]], "]"]]]]]]]]
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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> <mfrac> <mrow> <mo> ∂ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", "a", ")"]], "n"], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mo> ∂ </mo> <mi> n </mi> </mrow> </mfrac> <mo> ⩵ </mo> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", "a", ")"]], "n"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> n </ci> </bvar> <apply> <ci> Pochhammer </ci> <ci> a </ci> <ci> n </ci> </apply> </apply> <apply> <times /> <apply> <ci> Pochhammer </ci> <ci> a </ci> <ci> n </ci> </apply> <apply> <ci> PolyGamma </ci> <apply> <plus /> <ci> a </ci> <ci> n </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["n_"]]], RowBox[List["Pochhammer", "[", RowBox[List["a_", ",", "n_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["a", ",", "n"]], "]"]], " ", RowBox[List["PolyGamma", "[", RowBox[List["a", "+", "n"]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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