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.bjm4.01

 Input Form

 Hypergeometric2F1[-(25/8), 6, 15/8, z] == (1/68719476736) (1785 (-(262144/(-1 + z)) - (1/z^(7/8)) (42075 (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)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) - 6900300 (-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)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) + 56352450 (-(8/9) - 8 z + z^(9/8) (-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)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) - 125964300 (-(8/17) - (8 z)/9 - 8 z^2 + z^(17/8) (-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)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) + 81876795 (-(8/25) - (8 z)/17 - (8 z^2)/9 - 8 z^3 + 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)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 25 8 , 6 ; 15 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["25", "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["15", "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 7 / 8 ( 42075 ( log ( 1 - z 8 ) + log ( 1 - z 8 ) - log ( z 8 + 1 ) - log ( z 8 + 1 ) + - 1 4 log ( 1 - - 1 4 z 8 ) - - 1 4 log ( - 1 4 z 8 + 1 ) + ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) - 6900300 ( z 8 ( - log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) + log ( z 8 + 1 ) - - 1 4 log ( 1 - - 1 4 z 8 ) + - 1 4 log ( - 1 4 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) - 8 ) + 56352450 ( ( - log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) + log ( z 8 + 1 ) - - 1 4 log ( 1 - - 1 4 z 8 ) + - 1 4 log ( - 1 4 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) z 9 / 8 - 8 z - 8 9 ) - 125964300 ( ( - log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) + log ( z 8 + 1 ) - - 1 4 log ( 1 - - 1 4 z 8 ) + - 1 4 log ( - 1 4 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) z 17 / 8 - 8 z 2 - 8 z 9 - 8 17 ) + 81876795 ( ( - log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) + log ( z 8 + 1 ) - - 1 4 log ( 1 - - 1 4 z 8 ) + - 1 4 log ( - 1 4 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) z 25 / 8 - 8 z 3 - 8 z 2 9 - 8 z 17 - 8 25 ) - 262144 z - 1 ) ) HypergeometricPFQ -1 25 8 6 15 8 z 1 68719476736 1785 -1 1 z 7 8 -1 42075 1 -1 z 1 8 1 -1 z 1 8 -1 z 1 8 1 -1 z 1 8 1 -1 1 4 1 -1 -1 1 4 z 1 8 -1 -1 1 4 -1 1 4 z 1 8 1 -1 3 4 1 -1 -1 3 4 z 1 8 -1 -1 3 4 -1 3 4 z 1 8 1 -1 6900300 z 1 8 -1 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 z 1 8 1 -1 -1 1 4 1 -1 -1 1 4 z 1 8 -1 1 4 -1 1 4 z 1 8 1 -1 -1 3 4 1 -1 -1 3 4 z 1 8 -1 3 4 -1 3 4 z 1 8 1 -8 56352450 -1 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 z 1 8 1 -1 -1 1 4 1 -1 -1 1 4 z 1 8 -1 1 4 -1 1 4 z 1 8 1 -1 -1 3 4 1 -1 -1 3 4 z 1 8 -1 3 4 -1 3 4 z 1 8 1 z 9 8 -1 8 z -1 8 9 -1 125964300 -1 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 z 1 8 1 -1 -1 1 4 1 -1 -1 1 4 z 1 8 -1 1 4 -1 1 4 z 1 8 1 -1 -1 3 4 1 -1 -1 3 4 z 1 8 -1 3 4 -1 3 4 z 1 8 1 z 17 8 -1 8 z 2 -1 8 z 9 -1 -1 8 17 81876795 -1 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 z 1 8 1 -1 -1 1 4 1 -1 -1 1 4 z 1 8 -1 1 4 -1 1 4 z 1 8 1 -1 -1 3 4 1 -1 -1 3 4 z 1 8 -1 3 4 -1 3 4 z 1 8 1 z 25 8 -1 8 z 3 -1 8 z 2 9 -1 -1 8 z 17 -1 -1 8 25 -1 262144 z -1 -1 [/itex]

 Rule Form

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

 2007-05-02