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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.a88b.01

 Input Form

 Hypergeometric2F1[-(21/4), -(15/4), 3, z] == -((1/(48522699225 Pi z^2)) (64 Sqrt[1 + Sqrt[z]] (2 (306306 - 12711699 z - 1331614096 z^2 - 6628154265 z^3 - 7544875590 z^4 - 2116409477 z^5 - 84391692 z^6 + 1110417 z^7) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-612612 + 612612 Sqrt[z] + 24963939 z - 24963939 z^(3/2) + 1165545005 z^2 - 1165545005 z^(5/2) + 4087650750 z^3 - 4087650750 z^(7/2) + 3105383190 z^4 - 3105383190 z^(9/2) + 474329359 z^5 - 474329359 z^(11/2) + 1110417 z^6 - 1110417 z^(13/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])])))

 Standard Form

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 MathML Form

 2 F 1 ( - 21 4 , - 15 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["21", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", 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["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 48522699225 π z 2 ( 64 z + 1 ( 2 ( 1110417 z 7 - 84391692 z 6 - 2116409477 z 5 - 7544875590 z 4 - 6628154265 z 3 - 1331614096 z 2 - 12711699 z + 306306 ) E ( 2 z z + 1 ) + ( - 1110417 z 13 / 2 + 1110417 z 6 - 474329359 z 11 / 2 + 474329359 z 5 - 3105383190 z 9 / 2 + 3105383190 z 4 - 4087650750 z 7 / 2 + 4087650750 z 3 - 1165545005 z 5 / 2 + 1165545005 z 2 - 24963939 z 3 / 2 + 24963939 z + 612612 z - 612612 ) K ( 2 z z + 1 ) ) ) HypergeometricPFQ -1 21 4 -1 15 4 3 z -1 1 48522699225 z 2 -1 64 z 1 2 1 1 2 2 1110417 z 7 -1 84391692 z 6 -1 2116409477 z 5 -1 7544875590 z 4 -1 6628154265 z 3 -1 1331614096 z 2 -1 12711699 z 306306 EllipticE 2 z 1 2 z 1 2 1 -1 -1110417 z 13 2 1110417 z 6 -1 474329359 z 11 2 474329359 z 5 -1 3105383190 z 9 2 3105383190 z 4 -1 4087650750 z 7 2 4087650750 z 3 -1 1165545005 z 5 2 1165545005 z 2 -1 24963939 z 3 2 24963939 z 612612 z 1 2 -612612 EllipticK 2 z 1 2 z 1 2 1 -1 [/itex]

 Rule Form

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

 2007-05-02