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variants of this functions
Gamma






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[z] > Series representations > Generalized power series > Expansions of Gamma(-n+Epsilon) at Epsilon==0 > For the function itself





http://functions.wolfram.com/06.05.06.0032.01









  


  










Input Form





Gamma[-n + \[Epsilon]] \[Proportional] ((-1)^n/(n! \[Epsilon])) Sum[((Subscript[p, k] \[Epsilon]^q)/(q - k)!) (1 + Sum[Sum[(Binomial[n, j] (-1)^(j - 1))/j^i, {j, 1, n}] \[Epsilon]^i, {i, 1, Infinity}]), {q, 0, Infinity}, {k, 0, q}] /; Element[n, Integers] && n >= 0 && Subscript[s, 1] == EulerGamma && Subscript[s, k] == Zeta[k] /; k > 1 && Subscript[a, 0] == -EulerGamma && Subscript[a, k] == ((-1)^(k + 1)/(k + 1)) Subscript[s, k + 1] /; k > 0 && Subscript[p, 0] == (-1)^m EulerGamma^m && Subscript[p, k] == (1/(Subscript[a, 0] k)) Sum[(m j - k + j) Subscript[a, j] Subscript[p, k - j], {j, 1, k}] /; k > 0 && m = q - k










Standard Form





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MathML Form







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</mo> <mrow> <msub> <mi> a </mi> <mn> 0 </mn> </msub> <mo> &#63449; </mo> <mrow> <mo> - </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> &#63449; </mo> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> k </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <msub> <mi> s </mi> <mrow> <mi> k </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mrow> <mi> k </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> k </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> p </mi> <mn> 0 </mn> </msub> <mo> &#63449; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> m </mi> </msup> <mo> &#8290; 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</mo> <mi> m </mi> </mrow> </mrow> <mo> = </mo> <mrow> <mi> q </mi> <mo> - </mo> <mi> k </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Set </ci> <apply> <ci> Condition </ci> <apply> <ci> Condition </ci> <apply> <ci> Condition </ci> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <ci> &#1013; </ci> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <ci> n </ci> </apply> <ci> &#1013; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> q </ci> </uplimit> <apply> <sum /> <bvar> <ci> q </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> k </ci> </apply> <apply> <power /> <ci> &#1013; </ci> <ci> q </ci> </apply> <apply> <power /> <apply> <factorial /> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <sum /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> j </ci> </apply> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> j </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <ci> j </ci> <ci> i </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> &#1013; </ci> <ci> i </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <ci> &#8469; 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Rule Form





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





2007-05-02





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