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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/;m-n ∉ N && m ∈ N





http://functions.wolfram.com/06.10.06.0021.01









  


  








Input Form





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








Standard Form





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MathML Form







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Rule Form





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





2007-05-02