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.bt0c.01

 Input Form

 Hypergeometric2F1[-(9/8), 6, 23/8, -z] == (1/2147483648) (63 ((32768 (27 + 25 z))/(1 + z)^2 + (1/z^(7/8)) (126225 (-1)^(1/8) (Log[1 - (-1)^(1/8) z^(1/8)] - Log[1 + (-1)^(1/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(3/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(3/8) z^(1/8)] + I Log[1 - (-1)^(5/8) z^(1/8)] - I Log[1 + (-1)^(5/8) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(7/8) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(7/8) z^(1/8)])) + (1/z^(15/8)) (1275 (8 z^(7/8) - 7 (-1)^(1/8) Log[1 - (-1)^(1/8) z^(1/8)] + 7 (-1)^(1/8) Log[1 + (-1)^(1/8) z^(1/8)] - 7 (-1)^(3/8) Log[1 - (-1)^(3/8) z^(1/8)] + 7 (-1)^(3/8) Log[1 + (-1)^(3/8) z^(1/8)] - 7 (-1)^(5/8) Log[1 - (-1)^(5/8) z^(1/8)] + 7 (-1)^(5/8) Log[1 + (-1)^(5/8) z^(1/8)] - 7 (-1)^(7/8) Log[1 - (-1)^(7/8) z^(1/8)] + 7 (-1)^(7/8) Log[1 + (-1)^(7/8) z^(1/8)])) + (9392075/9) (-8 + 72 z + 9 (-1)^(1/8) z^(9/8) Log[1 - (-1)^(1/8) z^(1/8)] - 9 (-1)^(1/8) z^(9/8) Log[1 + (-1)^(1/8) z^(1/8)] + 9 (-1)^(3/8) z^(9/8) Log[1 - (-1)^(3/8) z^(1/8)] - 9 (-1)^(3/8) z^(9/8) Log[1 + (-1)^(3/8) z^(1/8)] + 9 (-1)^(5/8) z^(9/8) Log[1 - (-1)^(5/8) z^(1/8)] - 9 (-1)^(5/8) z^(9/8) Log[1 + (-1)^(5/8) z^(1/8)] + 9 (-1)^(7/8) z^(9/8) Log[1 - (-1)^(7/8) z^(1/8)] - 9 (-1)^(7/8) z^(9/8) Log[1 + (-1)^(7/8) z^(1/8)]) - 5175225 (-8 + (-1)^(1/8) z^(1/8) (-Log[1 - (-1)^(1/8) z^(1/8)] + Log[1 + (-1)^(1/8) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(3/8) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(3/8) z^(1/8)] - I Log[1 - (-1)^(5/8) z^(1/8)] + I Log[1 + (-1)^(5/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(7/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(7/8) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 9 8 , 6 ; 23 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["9", "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["23", "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 ( 63 ( 32768 ( 25 z + 27 ) ( z + 1 ) 2 + 1 z 7 / 8 ( 126225 - 1 8 ( log ( 1 - - 1 8 z 8 ) - log ( - 1 8 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - - 1 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 5 / 8 z 8 ) - log ( ( - 1 ) 5 / 8 z 8 + 1 ) + ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - ( - 1 ) 3 / 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) + 1 z 15 / 8 ( 1275 ( - 7 - 1 8 log ( 1 - - 1 8 z 8 ) + 7 - 1 8 log ( - 1 8 z 8 + 1 ) - 7 ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + 7 ( - 1 ) 3 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - 7 ( - 1 ) 5 / 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + 7 ( - 1 ) 5 / 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 7 ( - 1 ) 7 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 7 ( - 1 ) 7 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) + 8 z 7 / 8 ) ) + 9392075 9 ( 9 - 1 8 log ( 1 - - 1 8 z 8 ) z 9 / 8 - 9 - 1 8 log ( - 1 8 z 8 + 1 ) z 9 / 8 + 9 ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 9 / 8 - 9 ( - 1 ) 3 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 9 / 8 + 9 ( - 1 ) 5 / 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 9 / 8 - 9 ( - 1 ) 5 / 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 9 / 8 + 9 ( - 1 ) 7 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 9 / 8 - 9 ( - 1 ) 7 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 9 / 8 + 72 z - 8 ) - 5175225 ( - 1 8 z 8 ( - log ( 1 - - 1 8 z 8 ) + log ( - 1 8 z 8 + 1 ) - - 1 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + - 1 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 5 / 8 z 8 ) + log ( ( - 1 ) 5 / 8 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) - 8 ) ) ) HypergeometricPFQ -1 9 8 6 23 8 -1 z 1 2147483648 63 32768 25 z 27 z 1 2 -1 1 z 7 8 -1 126225 -1 1 8 1 -1 -1 1 8 z 1 8 -1 -1 1 8 z 1 8 1 -1 1 4 1 -1 -1 3 8 z 1 8 -1 -1 1 4 -1 3 8 z 1 8 1 1 -1 -1 5 8 z 1 8 -1 -1 5 8 z 1 8 1 -1 3 4 1 -1 -1 7 8 z 1 8 -1 -1 3 4 -1 7 8 z 1 8 1 1 z 15 8 -1 1275 -7 -1 1 8 1 -1 -1 1 8 z 1 8 7 -1 1 8 -1 1 8 z 1 8 1 -1 7 -1 3 8 1 -1 -1 3 8 z 1 8 7 -1 3 8 -1 3 8 z 1 8 1 -1 7 -1 5 8 1 -1 -1 5 8 z 1 8 7 -1 5 8 -1 5 8 z 1 8 1 -1 7 -1 7 8 1 -1 -1 7 8 z 1 8 7 -1 7 8 -1 7 8 z 1 8 1 8 z 7 8 9392075 9 9 -1 1 8 1 -1 -1 1 8 z 1 8 z 9 8 -1 9 -1 1 8 -1 1 8 z 1 8 1 z 9 8 9 -1 3 8 1 -1 -1 3 8 z 1 8 z 9 8 -1 9 -1 3 8 -1 3 8 z 1 8 1 z 9 8 9 -1 5 8 1 -1 -1 5 8 z 1 8 z 9 8 -1 9 -1 5 8 -1 5 8 z 1 8 1 z 9 8 9 -1 7 8 1 -1 -1 7 8 z 1 8 z 9 8 -1 9 -1 7 8 -1 7 8 z 1 8 1 z 9 8 72 z -8 -1 5175225 -1 1 8 z 1 8 -1 1 -1 -1 1 8 z 1 8 -1 1 8 z 1 8 1 -1 -1 1 4 1 -1 -1 3 8 z 1 8 -1 1 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 3 4 1 -1 -1 7 8 z 1 8 -1 3 4 -1 7 8 z 1 8 1 -8 [/itex]

 Rule Form

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

 2007-05-02