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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c5ky.01

 Input Form

 Hypergeometric2F1[15/8, 43/8, -(17/4), z] == -((-1209312 (1 + Sqrt[1 - z]) + 35568 (478 + 461 Sqrt[1 - z]) z - 342 (342567 + 319037 Sqrt[1 - z]) z^2 + 57 (9685996 + 8763517 Sqrt[1 - z]) z^3 - 399 (5752114 + 5157881 Sqrt[1 - z]) z^4 + 8778 (2441856 + 2331037 Sqrt[1 - z]) z^5 + 22 (1378740383 + 938844334 Sqrt[1 - z]) z^6 + 268345 (11740 + 673 Sqrt[1 - z]) z^7 - 268345 (978 + 71 Sqrt[1 - z]) z^8 + 195160 (137 + 6 Sqrt[1 - z]) z^9 - 1561280 z^10)/ (1209312 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (1 - z)^(23/2)))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["15", "8"], ",", FractionBox["43", "8"], ",", RowBox[List["-", FractionBox["17", "4"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "1209312"]], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]]]], "+", RowBox[List["35568", " ", RowBox[List["(", RowBox[List["478", "+", RowBox[List["461", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", "z"]], "-", RowBox[List["342", " ", RowBox[List["(", RowBox[List["342567", "+", RowBox[List["319037", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["57", " ", RowBox[List["(", RowBox[List["9685996", "+", RowBox[List["8763517", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["399", " ", RowBox[List["(", RowBox[List["5752114", "+", RowBox[List["5157881", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["8778", " ", RowBox[List["(", RowBox[List["2441856", "+", RowBox[List["2331037", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["22", " ", RowBox[List["(", RowBox[List["1378740383", "+", RowBox[List["938844334", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["268345", " ", RowBox[List["(", RowBox[List["11740", "+", RowBox[List["673", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["268345", " ", RowBox[List["(", RowBox[List["978", "+", RowBox[List["71", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["195160", " ", RowBox[List["(", RowBox[List["137", "+", RowBox[List["6", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["1561280", " ", SuperscriptBox["z", "10"]]]]], ")"]], "/", RowBox[List["(", RowBox[List["1209312", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["23", "/", "2"]]]]], ")"]]]]]]]]]]

 MathML Form

 2 F 1 ( 15 8 , 43 8 ; - 17 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["15", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["43", "8"], 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["17", "4"]]], 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] - ( - 1561280 z 10 + 195160 ( 6 1 - z + 137 ) z 9 - 268345 ( 71 1 - z + 978 ) z 8 + 268345 ( 673 1 - z + 11740 ) z 7 + 22 ( 938844334 1 - z + 1378740383 ) z 6 + 8778 ( 2331037 1 - z + 2441856 ) z 5 - 399 ( 5157881 1 - z + 5752114 ) z 4 + 57 ( 8763517 1 - z + 9685996 ) z 3 - 342 ( 319037 1 - z + 342567 ) z 2 + 35568 ( 461 1 - z + 478 ) z - 1209312 ( 1 - z + 1 ) ) / ( 1209312 2 4 ( 1 - z + 1 ) 3 / 4 ( 1 - z ) 23 / 2 ) HypergeometricPFQ 15 8 43 8 -1 17 4 z -1 -1561280 z 10 195160 6 1 -1 z 1 2 137 z 9 -1 268345 71 1 -1 z 1 2 978 z 8 268345 673 1 -1 z 1 2 11740 z 7 22 938844334 1 -1 z 1 2 1378740383 z 6 8778 2331037 1 -1 z 1 2 2441856 z 5 -1 399 5157881 1 -1 z 1 2 5752114 z 4 57 8763517 1 -1 z 1 2 9685996 z 3 -1 342 319037 1 -1 z 1 2 342567 z 2 35568 461 1 -1 z 1 2 478 z -1 1209312 1 -1 z 1 2 1 1209312 2 1 4 1 -1 z 1 2 1 3 4 1 -1 z 23 2 -1 [/itex]

 Rule Form

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

 2007-05-02