RamanujanTau[Subscript[p, j]^(n + 1)] == RamanujanTau[Subscript[p, j]] RamanujanTau[Subscript[p, j]^n] - Subscript[p, j]^11 RamanujanTau[Subscript[p, j]^(n - 1)] /; Element[Subscript[p, j], Primes] && n > 0

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamanujanTau", "[", SubsuperscriptBox["p", "j", RowBox[List["n", "+", "1"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["RamanujanTau", "[", SubscriptBox["p", "j"], "]"]], RowBox[List["RamanujanTau", "[", SubsuperscriptBox["p", "j", "n"], "]"]]]], "-", RowBox[List[SubsuperscriptBox["p", "j", "11"], RowBox[List["RamanujanTau", "[", SubsuperscriptBox["p", "j", RowBox[List["n", "-", "1"]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["p", "j"], "\[Element]", "Primes"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <semantics> <mi> &#964; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Tau]&quot;, RamanujanTau] </annotation> </semantics> <mo> ( </mo> <msubsup> <mi> p </mi> <mi> j </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mrow> <mrow> <semantics> <mi> &#964; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Tau]&quot;, RamanujanTau] </annotation> </semantics> <mo> ( </mo> <msub> <mi> p </mi> <mi> j </mi> </msub> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#964; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Tau]&quot;, RamanujanTau] </annotation> </semantics> <mo> ( </mo> <msubsup> <mi> p </mi> <mi> j </mi> <mi> n </mi> </msubsup> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msubsup> <mi> p </mi> <mi> j </mi> <mn> 11 </mn> </msubsup> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#964; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Tau]&quot;, RamanujanTau] </annotation> </semantics> <mo> ( </mo> <msubsup> <mi> p </mi> <mi> j </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> p </mi> <mi> j </mi> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8473; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalP]&quot;, Function[List[], Primes]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> RamanujanTau </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> </apply> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> RamanujanTau </ci> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> </apply> </apply> <apply> <ci> RamanujanTau </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> </apply> <ci> n </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> </apply> <cn type='integer'> 11 </cn> </apply> <apply> <ci> RamanujanTau </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> </apply> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> </apply> <primes /> </apply> <apply> <gt /> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2007-05-02