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.b5ts.01

 Input Form

 Hypergeometric2F1[-(47/8), 6, -(7/8), z] == (1/68719476736) (1306929 (262144/(-1 + z) - 23960365 (-(8/15) - (8 z)/7 + z^(15/8) (-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)])) + 262522260 (-(8/23) - (8 z)/15 - (8 z^2)/7 + z^(23/8) (-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)])) - 901890990 (-(8/31) - (8 z)/23 - (8 z^2)/15 - (8 z^3)/7 + z^(31/8) (-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)])) + 1217938260 (-(8/39) - (8 z)/31 - (8 z^2)/23 - (8 z^3)/15 - (8 z^4)/7 + z^(39/8) (-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)])) - 563620365 (-(8/47) - (8 z)/39 - (8 z^2)/31 - (8 z^3)/23 - (8 z^4)/15 - (8 z^5)/7 + z^(47/8) (-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 ( - 47 8 , 6 ; - 7 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["47", "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[RowBox[List["-", FractionBox["7", "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 ( 1306929 ( - 23960365 ( ( - 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 ) ) z 15 / 8 - 8 z 7 - 8 15 ) + 262522260 ( ( - 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 ) ) z 23 / 8 - 8 z 2 7 - 8 z 15 - 8 23 ) - 901890990 ( ( - 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 ) ) z 31 / 8 - 8 z 3 7 - 8 z 2 15 - 8 z 23 - 8 31 ) + 1217938260 ( ( - 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 ) ) z 39 / 8 - 8 z 4 7 - 8 z 3 15 - 8 z 2 23 - 8 z 31 - 8 39 ) - 563620365 ( ( - 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 ) ) z 47 / 8 - 8 z 5 7 - 8 z 4 15 - 8 z 3 23 - 8 z 2 31 - 8 z 39 - 8 47 ) + 262144 z - 1 ) ) HypergeometricPFQ -1 47 8 6 -1 7 8 z 1 68719476736 1306929 -23960365 -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 z 15 8 -1 8 z 7 -1 -1 8 15 262522260 -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 z 23 8 -1 8 z 2 7 -1 -1 8 z 15 -1 -1 8 23 -1 901890990 -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 z 31 8 -1 8 z 3 7 -1 -1 8 z 2 15 -1 -1 8 z 23 -1 -1 8 31 1217938260 -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 z 39 8 -1 8 z 4 7 -1 -1 8 z 3 15 -1 -1 8 z 2 23 -1 -1 8 z 31 -1 -1 8 39 -1 563620365 -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 z 47 8 -1 8 z 5 7 -1 -1 8 z 4 15 -1 -1 8 z 3 23 -1 -1 8 z 2 31 -1 -1 8 z 39 -1 -1 8 47 262144 z -1 -1 [/itex]

 Rule Form

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

 2007-05-02