html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.bu1e.01

 Input Form

 Hypergeometric2F1[-(7/8), 6, 33/8, z] == (1/68719476736) (1785 (262144/(-1 + z) - (1/z^(1/8)) (3892980 (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)])) - (1/z^(9/8)) (149730 (8 z^(1/8) + 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)])) - (1/z^(17/8)) (3220 (72 z^(1/8) + 8 z^(9/8) + 9 Log[1 - z^(1/8)] - 9 I Log[1 - I z^(1/8)] + 9 I Log[1 + I z^(1/8)] - 9 Log[1 + z^(1/8)] - 9 (-1)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] + 9 (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] - 9 (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] + 9 (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)])) + 5355 (-((8 (153 + 17 z + 9 z^2))/(153 z^3)) + (1/z^(25/8)) (-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)])) - 6534645 (-(8/7) + z^(7/8) (-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 ( - 7 8 , 6 ; 33 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["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["33", "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 68719476736 ( 1785 ( - 1 z 8 ( 3892980 ( 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 ) ) ) - 1 z 9 / 8 ( 149730 ( 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 z 8 ) ) - 1 z 17 / 8 ( 3220 ( 8 z 9 / 8 + 72 z 8 + 9 log ( 1 - z 8 ) - 9 log ( 1 - z 8 ) + 9 log ( z 8 + 1 ) - 9 log ( z 8 + 1 ) - 9 ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) + 9 ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) - 9 - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 9 - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) + 5355 ( 1 z 25 / 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 ( 9 z 2 + 17 z + 153 ) 153 z 3 ) - 6534645 ( z 7 / 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 7 ) + 262144 z - 1 ) ) HypergeometricPFQ -1 7 8 6 33 8 z 1 68719476736 1785 -1 1 z 1 8 -1 3892980 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 -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 1 z 9 8 -1 149730 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 -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 8 z 1 8 -1 1 z 17 8 -1 3220 8 z 9 8 72 z 1 8 9 1 -1 z 1 8 -1 9 1 -1 z 1 8 9 z 1 8 1 -1 9 z 1 8 1 -1 9 -1 3 4 1 -1 -1 1 4 z 1 8 9 -1 3 4 -1 1 4 z 1 8 1 -1 9 -1 1 4 1 -1 -1 3 4 z 1 8 9 -1 1 4 -1 3 4 z 1 8 1 5355 1 z 25 8 -1 -1 1 -1 z 1 8 1 -1 z 1 8 -1 z 1 8 1 z 1 8 1 -1 3 4 1 -1 -1 1 4 z 1 8 -1 -1 3 4 -1 1 4 z 1 8 1 -1 1 4 1 -1 -1 3 4 z 1 8 -1 -1 1 4 -1 3 4 z 1 8 1 -1 8 9 z 2 17 z 153 153 z 3 -1 -1 6534645 z 7 8 -1 1 -1 z 1 8 1 -1 z 1 8 -1 z 1 8 1 z 1 8 1 -1 3 4 1 -1 -1 1 4 z 1 8 -1 -1 3 4 -1 1 4 z 1 8 1 -1 1 4 1 -1 -1 3 4 z 1 8 -1 -1 1 4 -1 3 4 z 1 8 1 -1 8 7 262144 z -1 -1 [/itex]

 Rule Form

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

 2007-05-02