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.b5og.01

 Input Form

 Hypergeometric2F1[-(47/8), 5, -(15/8), -z] == (1/268435456) (435643 (8192/(1 + z) + 6351345 (-(8/31) + (8 z)/23 - (8 z^2)/15 + (8 z^3)/7 + (-1)^(1/8) z^(31/8) ((-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)])) + 6478395 (-(8/47) + (8 z)/39 - (8 z^2)/31 + (8 z^3)/23 - (8 z^4)/15 + (8 z^5)/7 + (-1)^(1/8) z^(47/8) ((-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)])) - 1041755 (-(8/23) + (8 z)/15 - (8 z^2)/7 + (-1)^(1/8) z^(23/8) ((-(-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)])) - 11562705 (-(8/39) + (8 z)/31 - (8 z^2)/23 + (8 z^3)/15 - (8 z^4)/7 + (-1)^(1/8) z^(39/8) ((-(-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)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 47 8 , 5 ; - 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["47", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", 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["15", "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 268435456 ( 435643 ( 6351345 ( - 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 ) ) z 31 / 8 + 8 z 3 7 - 8 z 2 15 + 8 z 23 - 8 31 ) + 6478395 ( - 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 ) ) z 47 / 8 + 8 z 5 7 - 8 z 4 15 + 8 z 3 23 - 8 z 2 31 + 8 z 39 - 8 47 ) - 1041755 ( - 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 ) ) z 23 / 8 - 8 z 2 7 + 8 z 15 - 8 23 ) - 11562705 ( - 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 ) ) z 39 / 8 - 8 z 4 7 + 8 z 3 15 - 8 z 2 23 + 8 z 31 - 8 39 ) + 8192 z + 1 ) ) HypergeometricPFQ -1 47 8 5 -1 15 8 -1 z 1 268435456 435643 6351345 -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 z 31 8 8 z 3 7 -1 -1 8 z 2 15 -1 8 z 23 -1 -1 8 31 6478395 -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 z 47 8 8 z 5 7 -1 -1 8 z 4 15 -1 8 z 3 23 -1 -1 8 z 2 31 -1 8 z 39 -1 -1 8 47 -1 1041755 -1 1 8 -1 -1 3 4 1 -1 -1 1 8 z 1 8 -1 3 4 -1 1 8 z 1 8 1 -1 1 -1 -1 3 8 z 1 8 -1 3 8 z 1 8 1 -1 -1 1 4 1 -1 -1 5 8 z 1 8 -1 1 4 -1 5 8 z 1 8 1 -1 1 -1 -1 7 8 z 1 8 -1 7 8 z 1 8 1 z 23 8 -1 8 z 2 7 -1 8 z 15 -1 -1 8 23 -1 11562705 -1 1 8 -1 -1 3 4 1 -1 -1 1 8 z 1 8 -1 3 4 -1 1 8 z 1 8 1 -1 1 -1 -1 3 8 z 1 8 -1 3 8 z 1 8 1 -1 -1 1 4 1 -1 -1 5 8 z 1 8 -1 1 4 -1 5 8 z 1 8 1 -1 1 -1 -1 7 8 z 1 8 -1 7 8 z 1 8 1 z 39 8 -1 8 z 4 7 -1 8 z 3 15 -1 -1 8 z 2 23 -1 8 z 31 -1 -1 8 39 8192 z 1 -1 [/itex]

 Rule Form

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

 2007-05-02