|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/02.03.08.0003.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Pi == 2 Product[Sec[Pi/2^k], {k, 2, Infinity}]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List["\[Pi]", "\[Equal]", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "2"]], "\[Infinity]"], RowBox[List["Sec", "[", FractionBox["\[Pi]", SuperscriptBox["2", "k"]], "]"]]]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mi> π </mi> <mo> ⩵ </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <mi> sec </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> π </mi> <msup> <mn> 2 </mn> <mi> k </mi> </msup> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <pi /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <sec /> <apply> <times /> <pi /> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "\[Pi]", "]"]], "\[RuleDelayed]", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "2"]], "\[Infinity]"], RowBox[List["Sec", "[", FractionBox["\[Pi]", SuperscriptBox["2", "k"]], "]"]]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|