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Pochhammer




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Pochhammer[a,n] > Series representations > Generalized power series > Expansions of (-m+Epsilon)n at Epsilon==0/;n ∈ Z && n<=m && m ∈ N





http://functions.wolfram.com/06.10.06.0026.01









  


  








Input Form





Pochhammer[-m + \[Epsilon], n] \[Proportional] (((-1)^n m!)/(m - n)!) (1 + \[Epsilon] (-PolyGamma[1 + m] + PolyGamma[1 + m - n]) + (1/2) \[Epsilon]^2 (PolyGamma[1 + m]^2 - 2 PolyGamma[1 + m] PolyGamma[1 + m - n] + PolyGamma[1 + m - n]^2 + PolyGamma[1, 1 + m] - PolyGamma[1, 1 + m - n]) - (1/6) \[Epsilon]^3 (PolyGamma[1 + m]^3 - 3 PolyGamma[1 + m]^2 PolyGamma[1 + m - n] - PolyGamma[1 + m - n]^3 - 3 PolyGamma[1 + m - n] (PolyGamma[1, 1 + m] - PolyGamma[1, 1 + m - n]) + 3 PolyGamma[1 + m] (PolyGamma[1 + m - n]^2 + PolyGamma[1, 1 + m] - PolyGamma[1, 1 + m - n]) + PolyGamma[2, 1 + m] - PolyGamma[2, 1 + m - n]) + O[\[Epsilon]^4]) /; Element[n, Integers] && n <= m && Element[m, Integers] && m >= 0








Standard Form





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MathML Form







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</mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msup> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; 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</ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> &#1013; </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <integers /> </apply> <apply> <leq /> <ci> n </ci> <ci> m </ci> </apply> <apply> <in /> <ci> m </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02