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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 4 and fixed z > For fixed z and a=13/4, b>=a > For fixed z and a=13/4, b=17/4





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









  


  








Input Form





Hypergeometric2F1[13/4, 17/4, 5/2, z] == (1/(2925 Pi^(3/2) z^(3/2))) (4 ((2 (-42 + 609 z + 1436 z^2 + 45 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/ (-1 + z)^5 - (2 (-42 + 609 z + 1436 z^2 + 45 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^5 - ((-42 + 21 Sqrt[z] + 588 z + 446 z^(3/2) + 990 z^2 + 45 z^(5/2)) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^4) + ((42 + 21 Sqrt[z] - 588 z + 446 z^(3/2) - 990 z^2 + 45 z^(5/2)) EllipticK[(1/2) (1 + Sqrt[z])])/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^5)) Gamma[3/4]^2)








Standard Form





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MathML Form







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<cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["13", "4"], ",", FractionBox["17", "4"], ",", FractionBox["5", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "42"]], "+", RowBox[List["609", " ", "z"]], "+", RowBox[List["1436", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["45", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "5"]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "42"]], "+", RowBox[List["609", " ", "z"]], "+", RowBox[List["1436", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["45", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "5"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "42"]], "+", RowBox[List["21", " ", SqrtBox["z"]]], "+", RowBox[List["588", " ", "z"]], "+", RowBox[List["446", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["990", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["45", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "4"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["42", "+", RowBox[List["21", " ", SqrtBox["z"]]], "-", RowBox[List["588", " ", "z"]], "+", RowBox[List["446", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["990", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["45", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "5"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], RowBox[List["2925", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]]]]]


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





2007-05-02