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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(7/8), 3, 17/8, -z] == -((1/(131072 z^(9/8))) (9 (-1)^(1/8) (392 (-1)^(7/8) z^(1/8) + 2760 (-1)^(7/8) z^(9/8) - 7 (-1)^(3/4) (-7 + 210 z + 345 z^2) Log[1 - (-1)^(1/8) z^(1/8)] + 7 (-1)^(3/4) (-7 + 210 z + 345 z^2) Log[1 + (-1)^(1/8) z^(1/8)] + 49 I Log[1 - (-1)^(3/8) z^(1/8)] - 1470 I z Log[1 - (-1)^(3/8) z^(1/8)] - 2415 I z^2 Log[1 - (-1)^(3/8) z^(1/8)] - 49 I Log[1 + (-1)^(3/8) z^(1/8)] + 1470 I z Log[1 + (-1)^(3/8) z^(1/8)] + 2415 I z^2 Log[1 + (-1)^(3/8) z^(1/8)] + 49 (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] - 1470 (-1)^(1/4) z Log[1 - (-1)^(5/8) z^(1/8)] - 2415 (-1)^(1/4) z^2 Log[1 - (-1)^(5/8) z^(1/8)] - 49 (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] + 1470 (-1)^(1/4) z Log[1 + (-1)^(5/8) z^(1/8)] + 2415 (-1)^(1/4) z^2 Log[1 + (-1)^(5/8) z^(1/8)] + 49 Log[1 - (-1)^(7/8) z^(1/8)] - 1470 z Log[1 - (-1)^(7/8) z^(1/8)] - 2415 z^2 Log[1 - (-1)^(7/8) z^(1/8)] - 49 Log[1 + (-1)^(7/8) z^(1/8)] + 1470 z Log[1 + (-1)^(7/8) z^(1/8)] + 2415 z^2 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( - 7 8 , 3 ; 17 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["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["17", "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 131072 z 9 / 8 ( 9 - 1 8 ( - 2415 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 + 2415 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 - 2415 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 + 2415 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 - 2415 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 + 2415 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 2760 ( - 1 ) 7 / 8 z 9 / 8 - 1470 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z + 1470 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z - 1470 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z + 1470 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z - 1470 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z + 1470 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 392 ( - 1 ) 7 / 8 z 8 - 7 ( - 1 ) 3 / 4 ( 345 z 2 + 210 z - 7 ) log ( 1 - - 1 8 z 8 ) + 7 ( - 1 ) 3 / 4 ( 345 z 2 + 210 z - 7 ) log ( - 1 8 z 8 + 1 ) + 49 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 49 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 49 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 49 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 49 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 49 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ -1 7 8 3 17 8 -1 z -1 1 131072 z 9 8 -1 9 -1 1 8 -2415 1 -1 -1 3 8 z 1 8 z 2 2415 -1 3 8 z 1 8 1 z 2 -1 2415 -1 1 4 1 -1 -1 5 8 z 1 8 z 2 2415 -1 1 4 -1 5 8 z 1 8 1 z 2 -1 2415 1 -1 -1 7 8 z 1 8 z 2 2415 -1 7 8 z 1 8 1 z 2 2760 -1 7 8 z 9 8 -1 1470 1 -1 -1 3 8 z 1 8 z 1470 -1 3 8 z 1 8 1 z -1 1470 -1 1 4 1 -1 -1 5 8 z 1 8 z 1470 -1 1 4 -1 5 8 z 1 8 1 z -1 1470 1 -1 -1 7 8 z 1 8 z 1470 -1 7 8 z 1 8 1 z 392 -1 7 8 z 1 8 -1 7 -1 3 4 345 z 2 210 z -7 1 -1 -1 1 8 z 1 8 7 -1 3 4 345 z 2 210 z -7 -1 1 8 z 1 8 1 49 1 -1 -1 3 8 z 1 8 -1 49 -1 3 8 z 1 8 1 49 -1 1 4 1 -1 -1 5 8 z 1 8 -1 49 -1 1 4 -1 5 8 z 1 8 1 49 1 -1 -1 7 8 z 1 8 -1 49 -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