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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c4ua.01

 Input Form

 Hypergeometric2F1[13/8, 6, 37/8, z] == (1/1342177280) (2639 (-((2048 (295 - 330 z + 99 z^2))/(-1 + z)^3) + (1/z^(21/8)) (1254 (104 z^(5/8) + 40 z^(13/8) + 65 Log[1 - z^(1/8)] - 65 I Log[1 - I z^(1/8)] + 65 I Log[1 + I z^(1/8)] - 65 Log[1 + z^(1/8)] + 65 (-1)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] - 65 (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] + 65 (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] - 65 (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)])) + (1/z^(13/8)) (16929 (8 z^(5/8) + 5 Log[1 - z^(1/8)] - 5 I Log[1 - I z^(1/8)] + 5 I Log[1 + I z^(1/8)] - 5 Log[1 + z^(1/8)] + 5 (-1)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] - 5 (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] + 5 (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] - 5 (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)])) - 45045 (-((8 (273 + 105 z + 65 z^2))/(1365 z^3)) + (1/z^(29/8)) (-Log[1 - z^(1/8)] + I Log[1 - I z^(1/8)] - I Log[1 + I z^(1/8)] + Log[1 + z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 13 8 , 6 ; 37 8 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["13", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["37", "8"], 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 1342177280 ( 2639 ( - 2048 ( 99 z 2 - 330 z + 295 ) ( z - 1 ) 3 + 1 z 21 / 8 ( 1254 ( 40 z 13 / 8 + 104 z 5 / 8 + 65 log ( 1 - z 8 ) - 65 log ( 1 - z 8 ) + 65 log ( z 8 + 1 ) - 65 log ( z 8 + 1 ) + 65 ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) - 65 ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) + 65 - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 65 - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) + 1 z 13 / 8 ( 16929 ( 5 log ( 1 - z 8 ) - 5 log ( 1 - z 8 ) + 5 log ( z 8 + 1 ) - 5 log ( z 8 + 1 ) + 5 ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) - 5 ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) + 5 - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 5 - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 8 z 5 / 8 ) ) - 45045 ( 1 z 29 / 8 ( - log ( 1 - z 8 ) + log ( 1 - z 8 ) - log ( z 8 + 1 ) + log ( z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) + ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) - - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) - 8 ( 65 z 2 + 105 z + 273 ) 1365 z 3 ) ) ) HypergeometricPFQ 13 8 6 37 8 z 1 1342177280 2639 -1 2048 99 z 2 -1 330 z 295 z -1 3 -1 1 z 21 8 -1 1254 40 z 13 8 104 z 5 8 65 1 -1 z 1 8 -1 65 1 -1 z 1 8 65 z 1 8 1 -1 65 z 1 8 1 65 -1 3 4 1 -1 -1 1 4 z 1 8 -1 65 -1 3 4 -1 1 4 z 1 8 1 65 -1 1 4 1 -1 -1 3 4 z 1 8 -1 65 -1 1 4 -1 3 4 z 1 8 1 1 z 13 8 -1 16929 5 1 -1 z 1 8 -1 5 1 -1 z 1 8 5 z 1 8 1 -1 5 z 1 8 1 5 -1 3 4 1 -1 -1 1 4 z 1 8 -1 5 -1 3 4 -1 1 4 z 1 8 1 5 -1 1 4 1 -1 -1 3 4 z 1 8 -1 5 -1 1 4 -1 3 4 z 1 8 1 8 z 5 8 -1 45045 1 z 29 8 -1 -1 1 -1 z 1 8 1 -1 z 1 8 -1 z 1 8 1 z 1 8 1 -1 -1 3 4 1 -1 -1 1 4 z 1 8 -1 3 4 -1 1 4 z 1 8 1 -1 -1 1 4 1 -1 -1 3 4 z 1 8 -1 1 4 -1 3 4 z 1 8 1 -1 8 65 z 2 105 z 273 1365 z 3 -1 [/itex]

 Rule Form

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

 2007-05-02