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variants of this functions
HarmonicNumber




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > HarmonicNumber[z] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations





http://functions.wolfram.com/06.16.16.0004.01









  


  








Input Form





HarmonicNumber[z + 1] == HarmonicNumber[z] + 1/(z + 1)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HarmonicNumber", "[", RowBox[List["z", "+", "1"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["HarmonicNumber", "[", "z", "]"]], "+", FractionBox["1", RowBox[List["z", "+", "1"]]]]]]]]]








MathML Form







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










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HarmonicNumber", "[", RowBox[List["z_", "+", "1"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["HarmonicNumber", "[", "z", "]"]], "+", FractionBox["1", RowBox[List["z", "+", "1"]]]]]]]]]


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





2001-10-29