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.byti.01

 Input Form

 Hypergeometric2F1[3/8, 2, 43/8, -z] == -((1/(2097152 z^(35/8))) (315 (-1)^(1/8) (45144 (-1)^(7/8) z^(3/8) + 114760 (-1)^(7/8) z^(11/8) + 82824 (-1)^(7/8) z^(19/8) + 5016 (-1)^(7/8) z^(27/8) - 627 I (1 + z)^3 (-27 + 5 z) Log[1 - (-1)^(1/8) z^(1/8)] + 627 I (1 + z)^3 (-27 + 5 z) Log[1 + (-1)^(1/8) z^(1/8)] - 16929 (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] - 47652 (-1)^(3/4) z Log[1 - (-1)^(3/8) z^(1/8)] - 41382 (-1)^(3/4) z^2 Log[1 - (-1)^(3/8) z^(1/8)] - 7524 (-1)^(3/4) z^3 Log[1 - (-1)^(3/8) z^(1/8)] + 3135 (-1)^(3/4) z^4 Log[1 - (-1)^(3/8) z^(1/8)] + 16929 (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] + 47652 (-1)^(3/4) z Log[1 + (-1)^(3/8) z^(1/8)] + 41382 (-1)^(3/4) z^2 Log[1 + (-1)^(3/8) z^(1/8)] + 7524 (-1)^(3/4) z^3 Log[1 + (-1)^(3/8) z^(1/8)] - 3135 (-1)^(3/4) z^4 Log[1 + (-1)^(3/8) z^(1/8)] - 16929 Log[1 - (-1)^(5/8) z^(1/8)] - 47652 z Log[1 - (-1)^(5/8) z^(1/8)] - 41382 z^2 Log[1 - (-1)^(5/8) z^(1/8)] - 7524 z^3 Log[1 - (-1)^(5/8) z^(1/8)] + 3135 z^4 Log[1 - (-1)^(5/8) z^(1/8)] + 16929 Log[1 + (-1)^(5/8) z^(1/8)] + 47652 z Log[1 + (-1)^(5/8) z^(1/8)] + 41382 z^2 Log[1 + (-1)^(5/8) z^(1/8)] + 7524 z^3 Log[1 + (-1)^(5/8) z^(1/8)] - 3135 z^4 Log[1 + (-1)^(5/8) z^(1/8)] + 16929 (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] + 47652 (-1)^(1/4) z Log[1 - (-1)^(7/8) z^(1/8)] + 41382 (-1)^(1/4) z^2 Log[1 - (-1)^(7/8) z^(1/8)] + 7524 (-1)^(1/4) z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 3135 (-1)^(1/4) z^4 Log[1 - (-1)^(7/8) z^(1/8)] - 16929 (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)] - 47652 (-1)^(1/4) z Log[1 + (-1)^(7/8) z^(1/8)] - 41382 (-1)^(1/4) z^2 Log[1 + (-1)^(7/8) z^(1/8)] - 7524 (-1)^(1/4) z^3 Log[1 + (-1)^(7/8) z^(1/8)] + 3135 (-1)^(1/4) z^4 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( 3 8 , 2 ; 43 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["3", "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["43", "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 35 / 8 ( 315 - 1 8 ( 3135 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 4 - 3135 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 4 + 3135 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 4 - 3135 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 4 - 3135 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 4 + 3135 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 4 + 5016 ( - 1 ) 7 / 8 z 27 / 8 - 7524 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 3 + 7524 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 3 - 7524 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 3 + 7524 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 3 + 7524 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 3 - 7524 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 3 + 82824 ( - 1 ) 7 / 8 z 19 / 8 - 41382 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 + 41382 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 - 41382 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 + 41382 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 + 41382 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 - 41382 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 114760 ( - 1 ) 7 / 8 z 11 / 8 - 47652 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z + 47652 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z - 47652 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z + 47652 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z + 47652 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z - 47652 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 45144 ( - 1 ) 7 / 8 z 3 / 8 - 627 ( z + 1 ) 3 ( 5 z - 27 ) log ( 1 - - 1 8 z 8 ) + 627 ( z + 1 ) 3 ( 5 z - 27 ) log ( - 1 8 z 8 + 1 ) - 16929 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + 16929 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - 16929 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + 16929 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 16929 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 16929 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ 3 8 2 43 8 -1 z -1 1 2097152 z 35 8 -1 315 -1 1 8 3135 -1 3 4 1 -1 -1 3 8 z 1 8 z 4 -1 3135 -1 3 4 -1 3 8 z 1 8 1 z 4 3135 1 -1 -1 5 8 z 1 8 z 4 -1 3135 -1 5 8 z 1 8 1 z 4 -1 3135 -1 1 4 1 -1 -1 7 8 z 1 8 z 4 3135 -1 1 4 -1 7 8 z 1 8 1 z 4 5016 -1 7 8 z 27 8 -1 7524 -1 3 4 1 -1 -1 3 8 z 1 8 z 3 7524 -1 3 4 -1 3 8 z 1 8 1 z 3 -1 7524 1 -1 -1 5 8 z 1 8 z 3 7524 -1 5 8 z 1 8 1 z 3 7524 -1 1 4 1 -1 -1 7 8 z 1 8 z 3 -1 7524 -1 1 4 -1 7 8 z 1 8 1 z 3 82824 -1 7 8 z 19 8 -1 41382 -1 3 4 1 -1 -1 3 8 z 1 8 z 2 41382 -1 3 4 -1 3 8 z 1 8 1 z 2 -1 41382 1 -1 -1 5 8 z 1 8 z 2 41382 -1 5 8 z 1 8 1 z 2 41382 -1 1 4 1 -1 -1 7 8 z 1 8 z 2 -1 41382 -1 1 4 -1 7 8 z 1 8 1 z 2 114760 -1 7 8 z 11 8 -1 47652 -1 3 4 1 -1 -1 3 8 z 1 8 z 47652 -1 3 4 -1 3 8 z 1 8 1 z -1 47652 1 -1 -1 5 8 z 1 8 z 47652 -1 5 8 z 1 8 1 z 47652 -1 1 4 1 -1 -1 7 8 z 1 8 z -1 47652 -1 1 4 -1 7 8 z 1 8 1 z 45144 -1 7 8 z 3 8 -1 627 z 1 3 5 z -27 1 -1 -1 1 8 z 1 8 627 z 1 3 5 z -27 -1 1 8 z 1 8 1 -1 16929 -1 3 4 1 -1 -1 3 8 z 1 8 16929 -1 3 4 -1 3 8 z 1 8 1 -1 16929 1 -1 -1 5 8 z 1 8 16929 -1 5 8 z 1 8 1 16929 -1 1 4 1 -1 -1 7 8 z 1 8 -1 16929 -1 1 4 -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