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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.afq6.01

 Input Form

 Hypergeometric2F1[-(3/2), 21/4, 3, z] == (1/(69615 Pi Sqrt[1 + Sqrt[1 - z]] z^2)) (4 Sqrt[2] ((1/(1 - z)^(3/4)) (2 (-144 - 1548 z + 61556 z^2 - 159467 z^3 + 100947 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)]) + (1/(1 - z)^(1/4)) (2 (-144 - 1548 z + 61556 z^2 - 159467 z^3 + 100947 z^4) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]) + (144 + 1620 z - 25916 z^2 + 33649 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1/(1 - z)^(3/4)) ((-144 - 1548 z + 61556 z^2 - 159467 z^3 + 100947 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]) - (1/Sqrt[1 - z]) ((-144 - 1548 z + 61556 z^2 - 159467 z^3 + 100947 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]) - (1/(1 - z)^(1/4)) ((-144 - 1548 z + 61556 z^2 - 159467 z^3 + 100947 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])))

 Standard Form

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 MathML Form

 2 F 1 ( - 3 2 , 21 4 ; 3 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["3", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["21", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["3", 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 69615 π 1 - z + 1 z 2 ( 4 2 ( 2 ( 100947 z 4 - 159467 z 3 + 61556 z 2 - 1548 z - 144 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) 1 - z 4 + 2 ( 100947 z 4 - 159467 z 3 + 61556 z 2 - 1548 z - 144 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ( 1 - z ) 3 / 4 + ( 33649 z 3 - 25916 z 2 + 1620 z + 144 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( 100947 z 4 - 159467 z 3 + 61556 z 2 - 1548 z - 144 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) 1 - z 4 - ( 100947 z 4 - 159467 z 3 + 61556 z 2 - 1548 z - 144 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) 1 - z - ( 100947 z 4 - 159467 z 3 + 61556 z 2 - 1548 z - 144 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ( 1 - z ) 3 / 4 ) ) HypergeometricPFQ -1 3 2 21 4 3 z 1 69615 1 -1 z 1 2 1 1 2 z 2 -1 4 2 1 2 2 100947 z 4 -1 159467 z 3 61556 z 2 -1 1548 z -144 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 4 -1 2 100947 z 4 -1 159467 z 3 61556 z 2 -1 1548 z -144 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 3 4 -1 33649 z 3 -1 25916 z 2 1620 z 144 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 100947 z 4 -1 159467 z 3 61556 z 2 -1 1548 z -144 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 4 -1 -1 100947 z 4 -1 159467 z 3 61556 z 2 -1 1548 z -144 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 2 -1 -1 100947 z 4 -1 159467 z 3 61556 z 2 -1 1548 z -144 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 3 4 -1 [/itex]

 Rule Form

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

 2007-05-02