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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.a8wk.01

 Input Form

 Hypergeometric2F1[-(21/4), 21/4, -(7/2), z] == (1/32) ((1/(1 + Sqrt[z])^(7/2)) (16 + 56 Sqrt[z] + 196 z + 476 z^(3/2) + 1225 z^2 + 2618 z^(5/2) + 6468 z^3 + 13728 z^(7/2) + 48048 z^4 + 219296 z^(9/2) + 335104 z^5 - 157696 z^(11/2) - 847616 z^6 - 749056 z^(13/2) - 214016 z^7) + (1/(1 - Sqrt[z])^(7/2)) (16 - 56 Sqrt[z] + 196 z - 476 z^(3/2) + 1225 z^2 - 2618 z^(5/2) + 6468 z^3 - 13728 z^(7/2) + 48048 z^4 - 219296 z^(9/2) + 335104 z^5 + 157696 z^(11/2) - 847616 z^6 + 749056 z^(13/2) - 214016 z^7))

 Standard Form

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 MathML Form

 2 F 1 ( - 21 4 , 21 4 ; - 7 2 ; 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[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[RowBox[List["-", FractionBox["7", "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 32 ( 1 ( z + 1 ) 7 / 2 ( - 214016 z 7 - 749056 z 13 / 2 - 847616 z 6 - 157696 z 11 / 2 + 335104 z 5 + 219296 z 9 / 2 + 48048 z 4 + 13728 z 7 / 2 + 6468 z 3 + 2618 z 5 / 2 + 1225 z 2 + 476 z 3 / 2 + 196 z + 56 z + 16 ) + 1 ( 1 - z ) 7 / 2 ( - 214016 z 7 + 749056 z 13 / 2 - 847616 z 6 + 157696 z 11 / 2 + 335104 z 5 - 219296 z 9 / 2 + 48048 z 4 - 13728 z 7 / 2 + 6468 z 3 - 2618 z 5 / 2 + 1225 z 2 - 476 z 3 / 2 + 196 z - 56 z + 16 ) ) HypergeometricPFQ -1 21 4 21 4 -1 7 2 z 1 32 1 z 1 2 1 7 2 -1 -214016 z 7 -1 749056 z 13 2 -1 847616 z 6 -1 157696 z 11 2 335104 z 5 219296 z 9 2 48048 z 4 13728 z 7 2 6468 z 3 2618 z 5 2 1225 z 2 476 z 3 2 196 z 56 z 1 2 16 1 1 -1 z 1 2 7 2 -1 -214016 z 7 749056 z 13 2 -1 847616 z 6 157696 z 11 2 335104 z 5 -1 219296 z 9 2 48048 z 4 -1 13728 z 7 2 6468 z 3 -1 2618 z 5 2 1225 z 2 -1 476 z 3 2 196 z -1 56 z 1 2 16 [/itex]

 Rule Form

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

 2007-05-02