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variants of this functions
JacobiP






Mathematica Notation

Traditional Notation









Polynomials > JacobiP[n,a,b,z] > Series representations > Generalized power series > Expansions at generic point a==a0 > For the function itself





http://functions.wolfram.com/05.06.06.0023.01









  


  










Input Form





JacobiP[n, a, b, z] == (1/n!) Sum[(Pochhammer[-n, h]/(k! h!)) ((1 - z)/2)^h Sum[(-1)^(i + j + n) j! (1 + Subscript[a, 0] + h)^(j - k) (1 + Subscript[a, 0] + b + n)^i StirlingS1[h, i] StirlingS1[-h + n, j] Hypergeometric2F1Regularized[-i, -k, 1 + j - k, (1 + Subscript[a, 0] + h)/(1 + Subscript[a, 0] + b + n)] (a - Subscript[a, 0])^k, {i, 0, h}, {j, 0, n - h}], {k, 0, Infinity}, {h, 0, n}]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiP", "[", RowBox[List["n_", ",", "a_", ",", "b_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "n"], FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "n"]], ",", "h"]], "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", "z"]], "2"], ")"]], "h"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "h"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["n", "-", "h"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["i", "+", "j", "+", "n"]]], " ", RowBox[List["j", "!"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "0"], "+", "h"]], ")"]], RowBox[List["j", "-", "k"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "0"], "+", "b", "+", "n"]], ")"]], "i"], " ", RowBox[List["StirlingS1", "[", RowBox[List["h", ",", "i"]], "]"]], " ", RowBox[List["StirlingS1", "[", RowBox[List[RowBox[List[RowBox[List["-", "h"]], "+", "n"]], ",", "j"]], "]"]], " ", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List[RowBox[List["-", "i"]], ",", RowBox[List["-", "k"]], ",", RowBox[List["1", "+", "j", "-", "k"]], ",", FractionBox[RowBox[List["1", "+", SubscriptBox["aa", "0"], "+", "h"]], RowBox[List["1", "+", SubscriptBox["aa", "0"], "+", "b", "+", "n"]]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", SubscriptBox["aa", "0"]]], ")"]], "k"]]]]]]]]], RowBox[List[RowBox[List["k", "!"]], " ", RowBox[List["h", "!"]]]]]]]]], RowBox[List["n", "!"]]]]]]]










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





2007-05-02





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