HarmonicNumber[4, r] == 1 + 2^(-r) + 3^(-r) + 4^(-r)

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mn> 4 </mn> <mrow> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </msubsup> <mo> &#10869; </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mn> 2 </mn> <mrow> <mo> - </mo> <mi> r </mi> </mrow> </msup> <mo> + </mo> <msup> <mn> 3 </mn> <mrow> <mo> - </mo> <mi> r </mi> </mrow> </msup> <mo> + </mo> <msup> <mn> 4 </mn> <mrow> <mo> - </mo> <mi> r </mi> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HarmonicNumber </ci> <cn type='integer'> 4 </cn> <ci> r </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HarmonicNumber", "[", RowBox[List["4", ",", "r_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["1", "+", SuperscriptBox["2", RowBox[List["-", "r"]]], "+", SuperscriptBox["3", RowBox[List["-", "r"]]], "+", SuperscriptBox["4", RowBox[List["-", "r"]]]]]]]]]

2001-10-29