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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[11/4, 15/4, -(5/2), z] == (1/(7392 Pi^(3/2))) (((1/(-1 + z)^9) (2 (-1848 + 24024 z - 177485 z^2 + 1640100 z^3 + 5240250 z^4 + 1649644 z^5 + 13923 z^6) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^9) (2 (-1848 + 24024 z - 177485 z^2 + 1640100 z^3 + 5240250 z^4 + 1649644 z^5 + 13923 z^6) EllipticE[(1/2) (1 + Sqrt[z])]) - (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^8)) ((-1848 + 924 Sqrt[z] + 23100 z - 11165 z^(3/2) - 166320 z^2 + 78540 z^(5/2) + 1561560 z^3 + 1312050 z^(7/2) + 3928200 z^4 + 702880 z^(9/2) + 946764 z^5 + 13923 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^9)) ((1848 + 924 Sqrt[z] - 23100 z - 11165 z^(3/2) + 166320 z^2 + 78540 z^(5/2) - 1561560 z^3 + 1312050 z^(7/2) - 3928200 z^4 + 702880 z^(9/2) - 946764 z^5 + 13923 z^(11/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["11", "4"], ",", FractionBox["15", "4"], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["7392", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "9"]], RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1848"]], "+", RowBox[List["24024", " ", "z"]], "-", RowBox[List["177485", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1640100", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5240250", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1649644", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["13923", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "9"]], RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1848"]], "+", RowBox[List["24024", " ", "z"]], "-", RowBox[List["177485", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1640100", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5240250", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1649644", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["13923", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "9"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "8"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1848"]], "+", RowBox[List["924", " ", SqrtBox["z"]]], "+", RowBox[List["23100", " ", "z"]], "-", RowBox[List["11165", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["166320", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["78540", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["1561560", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1312050", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["3928200", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["702880", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["946764", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["13923", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "8"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "9"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1848", "+", RowBox[List["924", " ", SqrtBox["z"]]], "-", RowBox[List["23100", " ", "z"]], "-", RowBox[List["11165", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["166320", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["78540", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["1561560", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1312050", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["3928200", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["702880", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["946764", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["13923", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 11 4 , 15 4 ; - 5 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["11", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["15", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 7392 π 3 / 2 ( ( 1 ( z - 1 ) 9 2 ( 13923 z 6 + 1649644 z 5 + 5240250 z 4 + 1640100 z 3 - 177485 z 2 + 24024 z - 1848 ) E ( 1 2 ( 1 - z ) ) + 1 ( z - 1 ) 9 2 ( 13923 z 6 + 1649644 z 5 + 5240250 z 4 + 1640100 z 3 - 177485 z 2 + 24024 z - 1848 ) E ( 1 2 ( z + 1 ) ) - 1 ( z - 1 ) 9 ( z + 1 ) 8 ( ( 13923 z 11 / 2 + 946764 z 5 + 702880 z 9 / 2 + 3928200 z 4 + 1312050 z 7 / 2 + 1561560 z 3 + 78540 z 5 / 2 - 166320 z 2 - 11165 z 3 / 2 + 23100 z + 924 z - 1848 ) K ( 1 2 ( 1 - z ) ) ) - 1 ( z - 1 ) 8 ( z + 1 ) 9 ( ( 13923 z 11 / 2 - 946764 z 5 + 702880 z 9 / 2 - 3928200 z 4 + 1312050 z 7 / 2 - 1561560 z 3 + 78540 z 5 / 2 + 166320 z 2 - 11165 z 3 / 2 - 23100 z + 924 z + 1848 ) K ( 1 2 ( z + 1 ) ) ) ) Γ ( 1 4 ) 2 ) HypergeometricPFQ 11 4 15 4 -1 5 2 z 1 7392 3 2 -1 1 z -1 9 -1 2 13923 z 6 1649644 z 5 5240250 z 4 1640100 z 3 -1 177485 z 2 24024 z -1848 EllipticE 1 2 1 -1 z 1 2 1 z -1 9 -1 2 13923 z 6 1649644 z 5 5240250 z 4 1640100 z 3 -1 177485 z 2 24024 z -1848 EllipticE 1 2 z 1 2 1 -1 1 z 1 2 -1 9 z 1 2 1 8 -1 13923 z 11 2 946764 z 5 702880 z 9 2 3928200 z 4 1312050 z 7 2 1561560 z 3 78540 z 5 2 -1 166320 z 2 -1 11165 z 3 2 23100 z 924 z 1 2 -1848 EllipticK 1 2 1 -1 z 1 2 -1 1 z 1 2 -1 8 z 1 2 1 9 -1 13923 z 11 2 -1 946764 z 5 702880 z 9 2 -1 3928200 z 4 1312050 z 7 2 -1 1561560 z 3 78540 z 5 2 166320 z 2 -1 11165 z 3 2 -1 23100 z 924 z 1 2 1848 EllipticK 1 2 z 1 2 1 Gamma 1 4 2 [/itex]

 Rule Form

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

 2007-05-02