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.bzgt.01

 Input Form

 Hypergeometric2F1[3/8, 6, 35/8, -z] == (1/10737418240) (5643 ((32768 (15 + 13 z))/(1 + z)^2 - (1/z^(3/8)) (488215 (-1)^(1/8) ((-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/z^(19/8)) (1365 (-88 z^(3/8) + 24 z^(11/8) + 33 (-1)^(5/8) Log[1 - (-1)^(1/8) z^(1/8)] - 33 (-1)^(5/8) Log[1 + (-1)^(1/8) z^(1/8)] - 33 (-1)^(7/8) Log[1 - (-1)^(3/8) z^(1/8)] + 33 (-1)^(7/8) Log[1 + (-1)^(3/8) z^(1/8)] - 33 (-1)^(1/8) Log[1 - (-1)^(5/8) z^(1/8)] + 33 (-1)^(1/8) Log[1 + (-1)^(5/8) z^(1/8)] + 33 (-1)^(3/8) Log[1 - (-1)^(7/8) z^(1/8)] - 33 (-1)^(3/8) Log[1 + (-1)^(7/8) z^(1/8)])) + (1/z^(11/8)) (39585 (8 z^(3/8) - 3 (-1)^(5/8) Log[1 - (-1)^(1/8) z^(1/8)] + 3 (-1)^(5/8) Log[1 + (-1)^(1/8) z^(1/8)] + 3 (-1)^(7/8) Log[1 - (-1)^(3/8) z^(1/8)] - 3 (-1)^(7/8) Log[1 + (-1)^(3/8) z^(1/8)] + 3 (-1)^(1/8) Log[1 - (-1)^(5/8) z^(1/8)] - 3 (-1)^(1/8) Log[1 + (-1)^(5/8) z^(1/8)] - 3 (-1)^(3/8) Log[1 - (-1)^(7/8) z^(1/8)] + 3 (-1)^(3/8) Log[1 + (-1)^(7/8) z^(1/8)])) + (1/(3 z^(27/8))) (65 (1672 z^(3/8) - 456 z^(11/8) + 264 z^(19/8) - 627 (-1)^(5/8) Log[1 - (-1)^(1/8) z^(1/8)] + 627 (-1)^(5/8) Log[1 + (-1)^(1/8) z^(1/8)] + 627 (-1)^(7/8) Log[1 - (-1)^(3/8) z^(1/8)] - 627 (-1)^(7/8) Log[1 + (-1)^(3/8) z^(1/8)] + 627 (-1)^(1/8) Log[1 - (-1)^(5/8) z^(1/8)] - 627 (-1)^(1/8) Log[1 + (-1)^(5/8) z^(1/8)] - 627 (-1)^(3/8) Log[1 - (-1)^(7/8) z^(1/8)] + 627 (-1)^(3/8) Log[1 + (-1)^(7/8) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 3 8 , 6 ; 35 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["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["35", "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 10737418240 ( 5643 ( 32768 ( 13 z + 15 ) ( z + 1 ) 2 - 1 z 3 / 8 ( 488215 - 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 ) ) ) + 1 z 19 / 8 ( 1365 ( 24 z 11 / 8 - 88 z 3 / 8 + 33 ( - 1 ) 5 / 8 log ( 1 - - 1 8 z 8 ) - 33 ( - 1 ) 5 / 8 log ( - 1 8 z 8 + 1 ) - 33 ( - 1 ) 7 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + 33 ( - 1 ) 7 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - 33 - 1 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + 33 - 1 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 33 ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 33 ( - 1 ) 3 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) + 1 z 11 / 8 ( 39585 ( - 3 ( - 1 ) 5 / 8 log ( 1 - - 1 8 z 8 ) + 3 ( - 1 ) 5 / 8 log ( - 1 8 z 8 + 1 ) + 3 ( - 1 ) 7 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 3 ( - 1 ) 7 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 3 - 1 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 3 - 1 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 3 ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 3 ( - 1 ) 3 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) + 8 z 3 / 8 ) ) + 1 3 z 27 / 8 ( 65 ( 264 z 19 / 8 - 456 z 11 / 8 + 1672 z 3 / 8 - 627 ( - 1 ) 5 / 8 log ( 1 - - 1 8 z 8 ) + 627 ( - 1 ) 5 / 8 log ( - 1 8 z 8 + 1 ) + 627 ( - 1 ) 7 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 627 ( - 1 ) 7 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 627 - 1 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 627 - 1 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 627 ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 627 ( - 1 ) 3 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) ) ) HypergeometricPFQ 3 8 6 35 8 -1 z 1 10737418240 5643 32768 13 z 15 z 1 2 -1 -1 1 z 3 8 -1 488215 -1 1 8 -1 1 -1 -1 1 8 z 1 8 -1 1 8 z 1 8 1 -1 3 4 1 -1 -1 3 8 z 1 8 -1 -1 3 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 -1 1 4 1 -1 -1 7 8 z 1 8 -1 1 4 -1 7 8 z 1 8 1 1 z 19 8 -1 1365 24 z 11 8 -1 88 z 3 8 33 -1 5 8 1 -1 -1 1 8 z 1 8 -1 33 -1 5 8 -1 1 8 z 1 8 1 -1 33 -1 7 8 1 -1 -1 3 8 z 1 8 33 -1 7 8 -1 3 8 z 1 8 1 -1 33 -1 1 8 1 -1 -1 5 8 z 1 8 33 -1 1 8 -1 5 8 z 1 8 1 33 -1 3 8 1 -1 -1 7 8 z 1 8 -1 33 -1 3 8 -1 7 8 z 1 8 1 1 z 11 8 -1 39585 -3 -1 5 8 1 -1 -1 1 8 z 1 8 3 -1 5 8 -1 1 8 z 1 8 1 3 -1 7 8 1 -1 -1 3 8 z 1 8 -1 3 -1 7 8 -1 3 8 z 1 8 1 3 -1 1 8 1 -1 -1 5 8 z 1 8 -1 3 -1 1 8 -1 5 8 z 1 8 1 -1 3 -1 3 8 1 -1 -1 7 8 z 1 8 3 -1 3 8 -1 7 8 z 1 8 1 8 z 3 8 1 3 z 27 8 -1 65 264 z 19 8 -1 456 z 11 8 1672 z 3 8 -1 627 -1 5 8 1 -1 -1 1 8 z 1 8 627 -1 5 8 -1 1 8 z 1 8 1 627 -1 7 8 1 -1 -1 3 8 z 1 8 -1 627 -1 7 8 -1 3 8 z 1 8 1 627 -1 1 8 1 -1 -1 5 8 z 1 8 -1 627 -1 1 8 -1 5 8 z 1 8 1 -1 627 -1 3 8 1 -1 -1 7 8 z 1 8 627 -1 3 8 -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