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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 8 and fixed z and a<0 > For fixed z and a=-45/8, b>=a > For fixed z and a=-45/8, b=39/8





http://functions.wolfram.com/07.23.03.b76o.01









  


  










Input Form





Hypergeometric2F1[-(45/8), 39/8, 11/4, z] == (1/(1134168387 z^2)) (2 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (251082 + 7699848 z - 264505782 z^2 + 1601230884 z^3 - 4016080640 z^4 + 4958041088 z^5 - 2998927360 z^6 + 712245248 z^7 + (1/Sqrt[1 - z]) (-251082 - 7574307 z + 551929188 z^2 - 4683921063 z^3 + 16227302960 z^4 - 28827591936 z^5 + 27845509120 z^6 - 13954383872 z^7 + 2848980992 z^8)))










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["45", "8"]]], ",", FractionBox["39", "8"], ",", FractionBox["11", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", SuperscriptBox["2", RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["251082", "+", RowBox[List["7699848", " ", "z"]], "-", RowBox[List["264505782", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1601230884", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["4016080640", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["4958041088", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["2998927360", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["712245248", " ", SuperscriptBox["z", "7"]]], "+", FractionBox[RowBox[List[RowBox[List["-", "251082"]], "-", RowBox[List["7574307", " ", "z"]], "+", RowBox[List["551929188", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4683921063", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["16227302960", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["28827591936", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["27845509120", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["13954383872", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["2848980992", " ", SuperscriptBox["z", "8"]]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]], ")"]]]], RowBox[List["1134168387", " ", SuperscriptBox["z", "2"]]]]]]]]










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





2007-05-02