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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(7/8), 2, 25/8, -z] == -((1/(65536 z^(17/8))) (51 (-1)^(1/8) (504 (-1)^(7/8) z^(1/8) + 112 (-1)^(7/8) z^(9/8) + 120 (-1)^(7/8) z^(17/8) - 21 (-1)^(3/4) (1 + z)^2 (-3 + 5 z) Log[1 - (-1)^(1/8) z^(1/8)] + 21 (-1)^(3/4) (1 + z)^2 (-3 + 5 z) Log[1 + (-1)^(1/8) z^(1/8)] + 63 I Log[1 - (-1)^(3/8) z^(1/8)] + 21 I z Log[1 - (-1)^(3/8) z^(1/8)] - 147 I z^2 Log[1 - (-1)^(3/8) z^(1/8)] - 105 I z^3 Log[1 - (-1)^(3/8) z^(1/8)] - 63 I Log[1 + (-1)^(3/8) z^(1/8)] - 21 I z Log[1 + (-1)^(3/8) z^(1/8)] + 147 I z^2 Log[1 + (-1)^(3/8) z^(1/8)] + 105 I z^3 Log[1 + (-1)^(3/8) z^(1/8)] + 63 (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] + 21 (-1)^(1/4) z Log[1 - (-1)^(5/8) z^(1/8)] - 147 (-1)^(1/4) z^2 Log[1 - (-1)^(5/8) z^(1/8)] - 105 (-1)^(1/4) z^3 Log[1 - (-1)^(5/8) z^(1/8)] - 63 (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] - 21 (-1)^(1/4) z Log[1 + (-1)^(5/8) z^(1/8)] + 147 (-1)^(1/4) z^2 Log[1 + (-1)^(5/8) z^(1/8)] + 105 (-1)^(1/4) z^3 Log[1 + (-1)^(5/8) z^(1/8)] + 63 Log[1 - (-1)^(7/8) z^(1/8)] + 21 z Log[1 - (-1)^(7/8) z^(1/8)] - 147 z^2 Log[1 - (-1)^(7/8) z^(1/8)] - 105 z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 63 Log[1 + (-1)^(7/8) z^(1/8)] - 21 z Log[1 + (-1)^(7/8) z^(1/8)] + 147 z^2 Log[1 + (-1)^(7/8) z^(1/8)] + 105 z^3 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( - 7 8 , 2 ; 25 8 ; - 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["7", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["25", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "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 65536 z 17 / 8 ( 51 - 1 8 ( - 105 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 3 + 105 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 3 - 105 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 3 + 105 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 3 - 105 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 3 + 105 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 3 + 120 ( - 1 ) 7 / 8 z 17 / 8 - 147 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 + 147 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 - 147 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 + 147 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 - 147 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 + 147 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 112 ( - 1 ) 7 / 8 z 9 / 8 + 21 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z - 21 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z + 21 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z - 21 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z + 21 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z - 21 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 504 ( - 1 ) 7 / 8 z 8 - 21 ( - 1 ) 3 / 4 ( z + 1 ) 2 ( 5 z - 3 ) log ( 1 - - 1 8 z 8 ) + 21 ( - 1 ) 3 / 4 ( z + 1 ) 2 ( 5 z - 3 ) log ( - 1 8 z 8 + 1 ) + 63 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 63 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 63 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 63 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 63 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 63 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ -1 7 8 2 25 8 -1 z -1 1 65536 z 17 8 -1 51 -1 1 8 -105 1 -1 -1 3 8 z 1 8 z 3 105 -1 3 8 z 1 8 1 z 3 -1 105 -1 1 4 1 -1 -1 5 8 z 1 8 z 3 105 -1 1 4 -1 5 8 z 1 8 1 z 3 -1 105 1 -1 -1 7 8 z 1 8 z 3 105 -1 7 8 z 1 8 1 z 3 120 -1 7 8 z 17 8 -1 147 1 -1 -1 3 8 z 1 8 z 2 147 -1 3 8 z 1 8 1 z 2 -1 147 -1 1 4 1 -1 -1 5 8 z 1 8 z 2 147 -1 1 4 -1 5 8 z 1 8 1 z 2 -1 147 1 -1 -1 7 8 z 1 8 z 2 147 -1 7 8 z 1 8 1 z 2 112 -1 7 8 z 9 8 21 1 -1 -1 3 8 z 1 8 z -1 21 -1 3 8 z 1 8 1 z 21 -1 1 4 1 -1 -1 5 8 z 1 8 z -1 21 -1 1 4 -1 5 8 z 1 8 1 z 21 1 -1 -1 7 8 z 1 8 z -1 21 -1 7 8 z 1 8 1 z 504 -1 7 8 z 1 8 -1 21 -1 3 4 z 1 2 5 z -3 1 -1 -1 1 8 z 1 8 21 -1 3 4 z 1 2 5 z -3 -1 1 8 z 1 8 1 63 1 -1 -1 3 8 z 1 8 -1 63 -1 3 8 z 1 8 1 63 -1 1 4 1 -1 -1 5 8 z 1 8 -1 63 -1 1 4 -1 5 8 z 1 8 1 63 1 -1 -1 7 8 z 1 8 -1 63 -1 7 8 z 1 8 1 [/itex]

 Rule Form

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

 2007-05-02