6/Pi^2 == Product[1 - 1/Subscript[p, k]^2, {k, 1, Infinity}] /; Element[Subscript[p, k], Primes]

Cell[BoxData[RowBox[List[RowBox[List[FractionBox["6", SuperscriptBox["\[Pi]", "2"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["(", RowBox[List["1", "-", FractionBox["1", SubsuperscriptBox["p", "k", "2"]]]], ")"]]]]]], "/;", RowBox[List[SubscriptBox["p", "k"], "\[Element]", "Primes"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mn> 6 </mn> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mfrac> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <msubsup> <mi> p </mi> <mi> k </mi> <mn> 2 </mn> </msubsup> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <msub> <mi> p </mi> <mi> k </mi> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8473; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalP]&quot;, Function[Primes]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> k </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> k </ci> </apply> <primes /> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox["6", SuperscriptBox["\[Pi]", "2"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["(", RowBox[List["1", "-", FractionBox["1", SubsuperscriptBox["p", "k", "2"]]]], ")"]]]], "/;", RowBox[List[SubscriptBox["p", "k"], "\[Element]", "Primes"]]]]]]]]

2001-10-29