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.by98.01

 Input Form

 Hypergeometric2F1[1/8, 6, 33/8, -z] == (1/2147483648) (255 ((32768 (17 + 15 z))/(1 + z)^2 + (1/z^(1/8)) (973245 (-1)^(1/8) ((-1)^(3/4) Log[1 - (-1)^(1/8) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(1/8) z^(1/8)] + I Log[1 - (-1)^(3/8) z^(1/8)] - I Log[1 + (-1)^(3/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] + Log[1 - (-1)^(7/8) z^(1/8)] - Log[1 + (-1)^(7/8) z^(1/8)])) + (1/z^(17/8)) (2415 (-72 z^(1/8) + 8 z^(9/8) + 9 (-1)^(7/8) Log[1 - (-1)^(1/8) z^(1/8)] - 9 (-1)^(7/8) Log[1 + (-1)^(1/8) z^(1/8)] + 9 (-1)^(5/8) Log[1 - (-1)^(3/8) z^(1/8)] - 9 (-1)^(5/8) Log[1 + (-1)^(3/8) z^(1/8)] + 9 (-1)^(3/8) Log[1 - (-1)^(5/8) z^(1/8)] - 9 (-1)^(3/8) Log[1 + (-1)^(5/8) z^(1/8)] + 9 (-1)^(1/8) Log[1 - (-1)^(7/8) z^(1/8)] - 9 (-1)^(1/8) Log[1 + (-1)^(7/8) z^(1/8)])) + (1/z^(9/8)) (74865 (8 z^(1/8) - (-1)^(7/8) Log[1 - (-1)^(1/8) z^(1/8)] + (-1)^(7/8) Log[1 + (-1)^(1/8) z^(1/8)] - (-1)^(5/8) Log[1 - (-1)^(3/8) z^(1/8)] + (-1)^(5/8) Log[1 + (-1)^(3/8) z^(1/8)] - (-1)^(3/8) Log[1 - (-1)^(5/8) z^(1/8)] + (-1)^(3/8) Log[1 + (-1)^(5/8) z^(1/8)] - (-1)^(1/8) Log[1 - (-1)^(7/8) z^(1/8)] + (-1)^(1/8) Log[1 + (-1)^(7/8) z^(1/8)])) + (1/z^(25/8)) (35 (1224 z^(1/8) - 136 z^(9/8) + 72 z^(17/8) - 153 (-1)^(7/8) Log[1 - (-1)^(1/8) z^(1/8)] + 153 (-1)^(7/8) Log[1 + (-1)^(1/8) z^(1/8)] - 153 (-1)^(5/8) Log[1 - (-1)^(3/8) z^(1/8)] + 153 (-1)^(5/8) Log[1 + (-1)^(3/8) z^(1/8)] - 153 (-1)^(3/8) Log[1 - (-1)^(5/8) z^(1/8)] + 153 (-1)^(3/8) Log[1 + (-1)^(5/8) z^(1/8)] - 153 (-1)^(1/8) Log[1 - (-1)^(7/8) z^(1/8)] + 153 (-1)^(1/8) Log[1 + (-1)^(7/8) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 1 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[FractionBox["1", "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[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 2147483648 ( 255 ( 32768 ( 15 z + 17 ) ( z + 1 ) 2 + 1 z 8 ( 973245 - 1 8 ( ( - 1 ) 3 / 4 log ( 1 - - 1 8 z 8 ) - ( - 1 ) 3 / 4 log ( - 1 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 3 / 8 z 8 ) - log ( ( - 1 ) 3 / 8 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 7 / 8 z 8 ) - log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) + 1 z 17 / 8 ( 2415 ( 8 z 9 / 8 - 72 z 8 + 9 ( - 1 ) 7 / 8 log ( 1 - - 1 8 z 8 ) - 9 ( - 1 ) 7 / 8 log ( - 1 8 z 8 + 1 ) + 9 ( - 1 ) 5 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 9 ( - 1 ) 5 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 9 ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 9 ( - 1 ) 3 / 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 9 - 1 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 9 - 1 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) + 1 z 9 / 8 ( 74865 ( - ( - 1 ) 7 / 8 log ( 1 - - 1 8 z 8 ) + ( - 1 ) 7 / 8 log ( - 1 8 z 8 + 1 ) - ( - 1 ) 5 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + ( - 1 ) 5 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + ( - 1 ) 3 / 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - - 1 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + - 1 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) + 8 z 8 ) ) + 1 z 25 / 8 ( 35 ( 72 z 17 / 8 - 136 z 9 / 8 + 1224 z 8 - 153 ( - 1 ) 7 / 8 log ( 1 - - 1 8 z 8 ) + 153 ( - 1 ) 7 / 8 log ( - 1 8 z 8 + 1 ) - 153 ( - 1 ) 5 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + 153 ( - 1 ) 5 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - 153 ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + 153 ( - 1 ) 3 / 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 153 - 1 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 153 - 1 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) ) ) HypergeometricPFQ 1 8 6 33 8 -1 z 1 2147483648 255 32768 15 z 17 z 1 2 -1 1 z 1 8 -1 973245 -1 1 8 -1 3 4 1 -1 -1 1 8 z 1 8 -1 -1 3 4 -1 1 8 z 1 8 1 1 -1 -1 3 8 z 1 8 -1 -1 3 8 z 1 8 1 -1 1 4 1 -1 -1 5 8 z 1 8 -1 -1 1 4 -1 5 8 z 1 8 1 1 -1 -1 7 8 z 1 8 -1 -1 7 8 z 1 8 1 1 z 17 8 -1 2415 8 z 9 8 -1 72 z 1 8 9 -1 7 8 1 -1 -1 1 8 z 1 8 -1 9 -1 7 8 -1 1 8 z 1 8 1 9 -1 5 8 1 -1 -1 3 8 z 1 8 -1 9 -1 5 8 -1 3 8 z 1 8 1 9 -1 3 8 1 -1 -1 5 8 z 1 8 -1 9 -1 3 8 -1 5 8 z 1 8 1 9 -1 1 8 1 -1 -1 7 8 z 1 8 -1 9 -1 1 8 -1 7 8 z 1 8 1 1 z 9 8 -1 74865 -1 -1 7 8 1 -1 -1 1 8 z 1 8 -1 7 8 -1 1 8 z 1 8 1 -1 -1 5 8 1 -1 -1 3 8 z 1 8 -1 5 8 -1 3 8 z 1 8 1 -1 -1 3 8 1 -1 -1 5 8 z 1 8 -1 3 8 -1 5 8 z 1 8 1 -1 -1 1 8 1 -1 -1 7 8 z 1 8 -1 1 8 -1 7 8 z 1 8 1 8 z 1 8 1 z 25 8 -1 35 72 z 17 8 -1 136 z 9 8 1224 z 1 8 -1 153 -1 7 8 1 -1 -1 1 8 z 1 8 153 -1 7 8 -1 1 8 z 1 8 1 -1 153 -1 5 8 1 -1 -1 3 8 z 1 8 153 -1 5 8 -1 3 8 z 1 8 1 -1 153 -1 3 8 1 -1 -1 5 8 z 1 8 153 -1 3 8 -1 5 8 z 1 8 1 -1 153 -1 1 8 1 -1 -1 7 8 z 1 8 153 -1 1 8 -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