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variants of this functions
NorlundB




Mathematica Notation

Traditional Notation









Polynomials > NorlundB[n,α,z] > Series representations > Generalized power series > Expansions at generic point alpha==alpha0





http://functions.wolfram.com/05.17.06.0014.01









  


  








Input Form





NorlundB[n, \[Alpha], z] \[Proportional] NorlundB[n, Subscript[\[Alpha], 0], z] + Sum[Binomial[n, k] z^k Derivative[0, 1][NorlundB][n - k, Subscript[\[Alpha], 0]] (\[Alpha] - Subscript[\[Alpha], 0]), {k, 0, n}] + (1/2) Sum[Binomial[n, k] z^k Derivative[0, 2][NorlundB][ n - k, Subscript[\[Alpha], 0]] (\[Alpha] - Subscript[\[Alpha], 0])^2, {k, 0, n}] + \[Ellipsis] /; (\[Alpha] -> Subscript[\[Alpha], 0])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["NorlundB", "[", RowBox[List["n", ",", "\[Alpha]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["NorlundB", "[", RowBox[List["n", ",", SubscriptBox["\[Alpha]", "0"], ",", "z"]], "]"]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["n", ",", " ", "k"]], "]"]], SuperscriptBox["z", "k"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Derivative", "[", RowBox[List["0", ",", "1"]], "]"]], "[", "NorlundB", "]"]], "[", RowBox[List[RowBox[List["n", "-", "k"]], ",", SubscriptBox["\[Alpha]", "0"]]], "]"]], ")"]], RowBox[List["(", RowBox[List["\[Alpha]", "-", SubscriptBox["\[Alpha]", "0"]]], ")"]]]]]], "+", RowBox[List[FractionBox["1", "2"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["n", ",", " ", "k"]], "]"]], SuperscriptBox["z", "k"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Derivative", "[", RowBox[List["0", ",", "2"]], "]"]], "[", "NorlundB", "]"]], "[", RowBox[List[RowBox[List["n", "-", "k"]], ",", SubscriptBox["\[Alpha]", "0"]]], "]"]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["\[Alpha]", "-", SubscriptBox["\[Alpha]", "0"]]], ")"]], "2"]]]]]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List["\[Alpha]", "\[Rule]", SubscriptBox["\[Alpha]", "0"]]], ")"]]]]]]








MathML Form







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</ms> <apply> <ci> TagBox </ci> <apply> <ci> SubsuperscriptBox </ci> <apply> <ci> TagBox </ci> <ms> B </ms> <ci> NorlundB </ci> </apply> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> - </ms> <ms> k </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <ms> &#945; </ms> <ms> ) </ms> </list> </apply> </apply> <apply> <ci> InterpretTemplate </ci> <apply> <ci> Function </ci> <ci> $CellContext`e </ci> <apply> <ci> Zeta </ci> <ci> $CellContext`e </ci> </apply> </apply> </apply> </apply> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> &#8706; </ms> <ms> &#945; </ms> </list> </apply> </apply> <apply> <ci> SubscriptBox </ci> <ms> | </ms> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> &#10869; </ms> <apply> <ci> SubscriptBox </ci> <ms> &#945; </ms> <ms> 0 </ms> </apply> </list> </apply> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> &#945; 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</ms> <ms> 2 </ms> </apply> <apply> <ci> TagBox </ci> <apply> <ci> SubsuperscriptBox </ci> <apply> <ci> TagBox </ci> <ms> B </ms> <ci> NorlundB </ci> </apply> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> - </ms> <ms> k </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <ms> &#945; </ms> <ms> ) </ms> </list> </apply> </apply> <apply> <ci> InterpretTemplate </ci> <apply> <ci> Function </ci> <ci> $CellContext`e </ci> <apply> <ci> Zeta </ci> <ci> $CellContext`e </ci> </apply> </apply> </apply> </apply> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> &#8706; </ms> <apply> <ci> SuperscriptBox </ci> <ms> &#945; </ms> <ms> 2 </ms> </apply> </list> </apply> </apply> <apply> <ci> SubscriptBox </ci> <ms> | </ms> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> &#10869; </ms> <apply> <ci> SubscriptBox </ci> <ms> &#945; </ms> <ms> 0 </ms> </apply> </list> </apply> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> &#945; </ms> <ms> 0 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <ms> 2 </ms> </apply> </list> </apply> </list> </apply> </list> </apply> <ms> + </ms> <ms> &#8230; </ms> </list> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> &#62754; </ms> <apply> <ci> SubscriptBox </ci> <ms> &#945; </ms> <ms> 0 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["NorlundB", "[", RowBox[List["n_", ",", "\[Alpha]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["NorlundB", "[", RowBox[List["n", ",", SubscriptBox["\[Alpha]\[Alpha]", "0"], ",", "z"]], "]"]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["n", ",", "k"]], "]"]], " ", SuperscriptBox["z", "k"], " ", RowBox[List[SuperscriptBox["NorlundB", TagBox[RowBox[List["(", RowBox[List["0", ",", "1"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[RowBox[List["n", "-", "k"]], ",", SubscriptBox["\[Alpha]\[Alpha]", "0"]]], "]"]], " ", RowBox[List["(", RowBox[List["\[Alpha]", "-", SubscriptBox["\[Alpha]\[Alpha]", "0"]]], ")"]]]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["n", ",", "k"]], "]"]], " ", SuperscriptBox["z", "k"], " ", RowBox[List[SuperscriptBox["NorlundB", TagBox[RowBox[List["(", RowBox[List["0", ",", "2"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[RowBox[List["n", "-", "k"]], ",", SubscriptBox["\[Alpha]\[Alpha]", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[Alpha]", "-", SubscriptBox["\[Alpha]\[Alpha]", "0"]]], ")"]], "2"]]]]]]], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["\[Alpha]", "\[Rule]", SubscriptBox["\[Alpha]\[Alpha]", "0"]]], ")"]]]]]]]]


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





2007-05-02