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Pochhammer






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.10.06.0018.01









  


  










Input Form





Pochhammer[a + \[Epsilon], n] \[Proportional] Pochhammer[a, n] (1 + \[Epsilon] (-PolyGamma[a] + PolyGamma[a + n]) + (\[Epsilon]^2/2) (PolyGamma[a]^2 - 2 PolyGamma[a] PolyGamma[a + n] + PolyGamma[a + n]^2 - PolyGamma[1, a] + PolyGamma[1, a + n]) - (\[Epsilon]^3/6) (PolyGamma[a]^3 - 3 PolyGamma[a]^2 PolyGamma[a + n] - PolyGamma[a + n]^3 + 3 PolyGamma[a + n] (PolyGamma[1, a] - PolyGamma[1, a + n]) + 3 PolyGamma[a] (PolyGamma[a + n]^2 - PolyGamma[1, a] + PolyGamma[1, a + n]) + PolyGamma[2, a] - PolyGamma[2, a + n]) + (\[Epsilon]^4/24) (PolyGamma[a]^4 - 4 PolyGamma[a]^3 PolyGamma[a + n] + PolyGamma[a + n]^4 + 3 PolyGamma[1, a]^2 - 6 PolyGamma[a + n]^2 (PolyGamma[1, a] - PolyGamma[1, a + n]) - 6 PolyGamma[1, a] PolyGamma[1, a + n] + 3 PolyGamma[1, a + n]^2 + 6 PolyGamma[a]^2 (PolyGamma[a + n]^2 - PolyGamma[1, a] + PolyGamma[1, a + n]) - 4 PolyGamma[a + n] (PolyGamma[2, a] - PolyGamma[2, a + n]) - 4 PolyGamma[a] (PolyGamma[a + n]^3 - 3 PolyGamma[a + n] (PolyGamma[1, a] - PolyGamma[1, a + n]) - PolyGamma[2, a] + PolyGamma[2, a + n]) - PolyGamma[3, a] + PolyGamma[3, a + n]) + O[\[Epsilon]^5]) /; !(Element[a, Integers] && a <= 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





© 1998- Wolfram Research, Inc.