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.cbeu.01

 Input Form

 Hypergeometric2F1[31/8, 4, 47/8, z] == (1/65536) (403 ((128 (-11 + 15 z))/(-1 + z)^2 + 10695 (-8 (1/(7 z^4) + 1/(15 z^3) + 1/(23 z^2) + 1/(31 z)) + (1/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)^(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)])) - 2415 (-((8 (345 + 161 z + 105 z^2))/(2415 z^3)) + (1/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)^(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 ( 31 8 , 4 ; 47 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["31", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["47", "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 65536 ( 403 ( 128 ( 15 z - 11 ) ( z - 1 ) 2 + 10695 ( 1 z 39 / 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 ( 1 31 z + 1 23 z 2 + 1 15 z 3 + 1 7 z 4 ) ) - 2415 ( 1 z 31 / 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 ( 105 z 2 + 161 z + 345 ) 2415 z 3 ) ) ) HypergeometricPFQ 31 8 4 47 8 z 1 65536 403 128 15 z -11 z -1 2 -1 10695 1 z 39 8 -1 -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 -1 8 1 31 z -1 1 23 z 2 -1 1 15 z 3 -1 1 7 z 4 -1 -1 2415 1 z 31 8 -1 -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 -1 8 105 z 2 161 z 345 2415 z 3 -1 [/itex]

 Rule Form

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

 2007-05-02