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.b6nz.01

 Input Form

 Hypergeometric2F1[-(45/8), 1, -(29/8), -z] == (1665/64) (64/1665 - (64 z)/1073 + (64 z^2)/609 - (64 z^3)/273 + (64 z^4)/65 + (8 z^5)/5 + (-1)^(1/8) z^(37/8) (I Log[1 - (-1)^(1/8) z^(1/8)] - I Log[1 + (-1)^(1/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] - Log[1 - (-1)^(5/8) z^(1/8)] + Log[1 + (-1)^(5/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)]) + (-1)^(1/8) z^(45/8) (I Log[1 - (-1)^(1/8) z^(1/8)] - I Log[1 + (-1)^(1/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] - Log[1 - (-1)^(5/8) z^(1/8)] + Log[1 + (-1)^(5/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 45 8 , 1 ; - 29 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["45", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["1", 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["29", "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] 1665 64 ( - 1 8 ( log ( 1 - - 1 8 z 8 ) - log ( - 1 8 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 5 / 8 z 8 ) + log ( ( - 1 ) 5 / 8 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 45 / 8 + 8 z 5 5 + - 1 8 ( log ( 1 - - 1 8 z 8 ) - log ( - 1 8 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 5 / 8 z 8 ) + log ( ( - 1 ) 5 / 8 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 37 / 8 + 64 z 4 65 - 64 z 3 273 + 64 z 2 609 - 64 z 1073 + 64 1665 ) HypergeometricPFQ -1 45 8 1 -1 29 8 -1 z 1665 64 -1 1 8 1 -1 -1 1 8 z 1 8 -1 -1 1 8 z 1 8 1 -1 -1 3 4 1 -1 -1 3 8 z 1 8 -1 3 4 -1 3 8 z 1 8 1 -1 1 -1 -1 5 8 z 1 8 -1 5 8 z 1 8 1 -1 1 4 1 -1 -1 7 8 z 1 8 -1 -1 1 4 -1 7 8 z 1 8 1 z 45 8 8 z 5 5 -1 -1 1 8 1 -1 -1 1 8 z 1 8 -1 -1 1 8 z 1 8 1 -1 -1 3 4 1 -1 -1 3 8 z 1 8 -1 3 4 -1 3 8 z 1 8 1 -1 1 -1 -1 5 8 z 1 8 -1 5 8 z 1 8 1 -1 1 4 1 -1 -1 7 8 z 1 8 -1 -1 1 4 -1 7 8 z 1 8 1 z 37 8 64 z 4 65 -1 -1 64 z 3 273 -1 64 z 2 609 -1 -1 64 z 1073 -1 64 1665 [/itex]

 Rule Form

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

 2007-05-02