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.bxlx.01

 Input Form

 Hypergeometric2F1[1/8, 2, 41/8, -z] == -((1/(2097152 z^(33/8))) (275 (-1)^(1/8) (30600 (-1)^(7/8) z^(1/8) + 79832 (-1)^(7/8) z^(9/8) + 58648 (-1)^(7/8) z^(17/8) + 1224 (-1)^(7/8) z^(25/8) - 153 (-1)^(3/4) (1 + z)^3 (-25 + 7 z) Log[1 - (-1)^(1/8) z^(1/8)] + 153 (-1)^(3/4) (1 + z)^3 (-25 + 7 z) Log[1 + (-1)^(1/8) z^(1/8)] + 3825 I Log[1 - (-1)^(3/8) z^(1/8)] + 10404 I z Log[1 - (-1)^(3/8) z^(1/8)] + 8262 I z^2 Log[1 - (-1)^(3/8) z^(1/8)] + 612 I z^3 Log[1 - (-1)^(3/8) z^(1/8)] - 1071 I z^4 Log[1 - (-1)^(3/8) z^(1/8)] - 3825 I Log[1 + (-1)^(3/8) z^(1/8)] - 10404 I z Log[1 + (-1)^(3/8) z^(1/8)] - 8262 I z^2 Log[1 + (-1)^(3/8) z^(1/8)] - 612 I z^3 Log[1 + (-1)^(3/8) z^(1/8)] + 1071 I z^4 Log[1 + (-1)^(3/8) z^(1/8)] + 3825 (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] + 10404 (-1)^(1/4) z Log[1 - (-1)^(5/8) z^(1/8)] + 8262 (-1)^(1/4) z^2 Log[1 - (-1)^(5/8) z^(1/8)] + 612 (-1)^(1/4) z^3 Log[1 - (-1)^(5/8) z^(1/8)] - 1071 (-1)^(1/4) z^4 Log[1 - (-1)^(5/8) z^(1/8)] - 3825 (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] - 10404 (-1)^(1/4) z Log[1 + (-1)^(5/8) z^(1/8)] - 8262 (-1)^(1/4) z^2 Log[1 + (-1)^(5/8) z^(1/8)] - 612 (-1)^(1/4) z^3 Log[1 + (-1)^(5/8) z^(1/8)] + 1071 (-1)^(1/4) z^4 Log[1 + (-1)^(5/8) z^(1/8)] + 3825 Log[1 - (-1)^(7/8) z^(1/8)] + 10404 z Log[1 - (-1)^(7/8) z^(1/8)] + 8262 z^2 Log[1 - (-1)^(7/8) z^(1/8)] + 612 z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 1071 z^4 Log[1 - (-1)^(7/8) z^(1/8)] - 3825 Log[1 + (-1)^(7/8) z^(1/8)] - 10404 z Log[1 + (-1)^(7/8) z^(1/8)] - 8262 z^2 Log[1 + (-1)^(7/8) z^(1/8)] - 612 z^3 Log[1 + (-1)^(7/8) z^(1/8)] + 1071 z^4 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( 1 8 , 2 ; 41 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["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["41", "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 2097152 z 33 / 8 ( 275 - 1 8 ( - 1071 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 4 + 1071 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 4 - 1071 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 4 + 1071 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 4 - 1071 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 4 + 1071 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 4 + 1224 ( - 1 ) 7 / 8 z 25 / 8 + 612 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 3 - 612 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 3 + 612 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 3 - 612 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 3 + 612 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 3 - 612 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 3 + 58648 ( - 1 ) 7 / 8 z 17 / 8 + 8262 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 - 8262 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 + 8262 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 - 8262 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 + 8262 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 - 8262 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 79832 ( - 1 ) 7 / 8 z 9 / 8 + 10404 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z - 10404 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z + 10404 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z - 10404 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z + 10404 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z - 10404 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 30600 ( - 1 ) 7 / 8 z 8 - 153 ( - 1 ) 3 / 4 ( z + 1 ) 3 ( 7 z - 25 ) log ( 1 - - 1 8 z 8 ) + 153 ( - 1 ) 3 / 4 ( z + 1 ) 3 ( 7 z - 25 ) log ( - 1 8 z 8 + 1 ) + 3825 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 3825 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 3825 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 3825 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 3825 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 3825 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ 1 8 2 41 8 -1 z -1 1 2097152 z 33 8 -1 275 -1 1 8 -1071 1 -1 -1 3 8 z 1 8 z 4 1071 -1 3 8 z 1 8 1 z 4 -1 1071 -1 1 4 1 -1 -1 5 8 z 1 8 z 4 1071 -1 1 4 -1 5 8 z 1 8 1 z 4 -1 1071 1 -1 -1 7 8 z 1 8 z 4 1071 -1 7 8 z 1 8 1 z 4 1224 -1 7 8 z 25 8 612 1 -1 -1 3 8 z 1 8 z 3 -1 612 -1 3 8 z 1 8 1 z 3 612 -1 1 4 1 -1 -1 5 8 z 1 8 z 3 -1 612 -1 1 4 -1 5 8 z 1 8 1 z 3 612 1 -1 -1 7 8 z 1 8 z 3 -1 612 -1 7 8 z 1 8 1 z 3 58648 -1 7 8 z 17 8 8262 1 -1 -1 3 8 z 1 8 z 2 -1 8262 -1 3 8 z 1 8 1 z 2 8262 -1 1 4 1 -1 -1 5 8 z 1 8 z 2 -1 8262 -1 1 4 -1 5 8 z 1 8 1 z 2 8262 1 -1 -1 7 8 z 1 8 z 2 -1 8262 -1 7 8 z 1 8 1 z 2 79832 -1 7 8 z 9 8 10404 1 -1 -1 3 8 z 1 8 z -1 10404 -1 3 8 z 1 8 1 z 10404 -1 1 4 1 -1 -1 5 8 z 1 8 z -1 10404 -1 1 4 -1 5 8 z 1 8 1 z 10404 1 -1 -1 7 8 z 1 8 z -1 10404 -1 7 8 z 1 8 1 z 30600 -1 7 8 z 1 8 -1 153 -1 3 4 z 1 3 7 z -25 1 -1 -1 1 8 z 1 8 153 -1 3 4 z 1 3 7 z -25 -1 1 8 z 1 8 1 3825 1 -1 -1 3 8 z 1 8 -1 3825 -1 3 8 z 1 8 1 3825 -1 1 4 1 -1 -1 5 8 z 1 8 -1 3825 -1 1 4 -1 5 8 z 1 8 1 3825 1 -1 -1 7 8 z 1 8 -1 3825 -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