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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c4qj.01

 Input Form

 Hypergeometric2F1[13/8, 41/8, 6, z] == (524288 2^(1/4) (-((1/(1 - z)^(3/4)) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-32768 + 18560 z + 4605 z^2 + 2360 z^3 + 1600 z^4) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])) - (32768 + 1920 z + 915 z^2 + 400 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1/(1 - z)^(3/4)) (Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-32768 + 18560 z + 4605 z^2 + 2360 z^3 + 1600 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) + ((-32768 + 18560 z + 4605 z^2 + 2360 z^3 + 1600 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])/ Sqrt[1 - z]))/(237429225 Pi (1 + Sqrt[1 - z])^(1/4) z^5)

 Standard Form

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 MathML Form

 2 F 1 ( 13 8 , 41 8 ; 6 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["13", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["41", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["6", 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] ( 524288 2 4 ( - 1 ( 1 - z ) 3 / 4 2 2 1 - z + 1 ( 1600 z 4 + 2360 z 3 + 4605 z 2 + 18560 z - 32768 ) E ( 1 2 - 1 - z 4 2 1 - z + 1 ) - ( 400 z 3 + 915 z 2 + 1920 z + 32768 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) + ( 1600 z 4 + 2360 z 3 + 4605 z 2 + 18560 z - 32768 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) 1 - z + 2 1 - z + 1 ( 1600 z 4 + 2360 z 3 + 4605 z 2 + 18560 z - 32768 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) ( 1 - z ) 3 / 4 ) ) / ( 237429225 π 1 - z + 1 4 z 5 ) HypergeometricPFQ 13 8 41 8 6 z 524288 2 1 4 -1 1 1 -1 z 3 4 -1 2 2 1 2 1 -1 z 1 2 1 1 2 1600 z 4 2360 z 3 4605 z 2 18560 z -32768 EllipticE 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 400 z 3 915 z 2 1920 z 32768 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 1600 z 4 2360 z 3 4605 z 2 18560 z -32768 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 1 -1 z 1 2 -1 2 1 2 1 -1 z 1 2 1 1 2 1600 z 4 2360 z 3 4605 z 2 18560 z -32768 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 1 -1 z 3 4 -1 237429225 1 -1 z 1 2 1 1 4 z 5 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["13", "8"], ",", FractionBox["41", "8"], ",", "6", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["524288", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "32768"]], "+", RowBox[List["18560", " ", "z"]], "+", RowBox[List["4605", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2360", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1600", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["32768", "+", RowBox[List["1920", " ", "z"]], "+", RowBox[List["915", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["400", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", FractionBox[RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "32768"]], "+", RowBox[List["18560", " ", "z"]], "+", RowBox[List["4605", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2360", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1600", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "32768"]], "+", RowBox[List["18560", " ", "z"]], "+", RowBox[List["4605", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2360", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1600", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]], ")"]]]], RowBox[List["237429225", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", "5"]]]]]]]]

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

 2007-05-02