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.c494.01

 Input Form

 Hypergeometric2F1[13/8, 2, 45/8, -z] == (1/(983040 z^(37/8))) (1073 (-1)^(1/8) (63336 (-1)^(7/8) z^(5/8) + 113232 (-1)^(7/8) z^(13/8) + 47336 (-1)^(7/8) z^(21/8) + 1365 (-1)^(1/4) (1 + z)^2 (29 + 5 z) Log[1 - (-1)^(1/8) z^(1/8)] - 1365 (-1)^(1/4) (1 + z)^2 (29 + 5 z) Log[1 + (-1)^(1/8) z^(1/8)] - 39585 Log[1 - (-1)^(3/8) z^(1/8)] - 85995 z Log[1 - (-1)^(3/8) z^(1/8)] - 53235 z^2 Log[1 - (-1)^(3/8) z^(1/8)] - 6825 z^3 Log[1 - (-1)^(3/8) z^(1/8)] + 39585 Log[1 + (-1)^(3/8) z^(1/8)] + 85995 z Log[1 + (-1)^(3/8) z^(1/8)] + 53235 z^2 Log[1 + (-1)^(3/8) z^(1/8)] + 6825 z^3 Log[1 + (-1)^(3/8) z^(1/8)] - 39585 (-1)^(3/4) Log[1 - (-1)^(5/8) z^(1/8)] - 85995 (-1)^(3/4) z Log[1 - (-1)^(5/8) z^(1/8)] - 53235 (-1)^(3/4) z^2 Log[1 - (-1)^(5/8) z^(1/8)] - 6825 (-1)^(3/4) z^3 Log[1 - (-1)^(5/8) z^(1/8)] + 39585 (-1)^(3/4) Log[1 + (-1)^(5/8) z^(1/8)] + 85995 (-1)^(3/4) z Log[1 + (-1)^(5/8) z^(1/8)] + 53235 (-1)^(3/4) z^2 Log[1 + (-1)^(5/8) z^(1/8)] + 6825 (-1)^(3/4) z^3 Log[1 + (-1)^(5/8) z^(1/8)] + 39585 I Log[1 - (-1)^(7/8) z^(1/8)] + 85995 I z Log[1 - (-1)^(7/8) z^(1/8)] + 53235 I z^2 Log[1 - (-1)^(7/8) z^(1/8)] + 6825 I z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 39585 I Log[1 + (-1)^(7/8) z^(1/8)] - 85995 I z Log[1 + (-1)^(7/8) z^(1/8)] - 53235 I z^2 Log[1 + (-1)^(7/8) z^(1/8)] - 6825 I z^3 Log[1 + (-1)^(7/8) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( 13 8 , 2 ; 45 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["13", "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["45", "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 983040 z 37 / 8 ( 1073 - 1 8 ( - 6825 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 3 + 6825 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 3 - 6825 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 3 + 6825 ( - 1 ) 3 / 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 3 + 6825 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 3 - 6825 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 3 + 47336 ( - 1 ) 7 / 8 z 21 / 8 - 53235 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 + 53235 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 - 53235 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 + 53235 ( - 1 ) 3 / 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 + 53235 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 - 53235 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 113232 ( - 1 ) 7 / 8 z 13 / 8 - 85995 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z + 85995 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z - 85995 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z + 85995 ( - 1 ) 3 / 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z + 85995 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z - 85995 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 63336 ( - 1 ) 7 / 8 z 5 / 8 + 1365 - 1 4 ( z + 1 ) 2 ( 5 z + 29 ) log ( 1 - - 1 8 z 8 ) - 1365 - 1 4 ( z + 1 ) 2 ( 5 z + 29 ) log ( - 1 8 z 8 + 1 ) - 39585 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + 39585 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - 39585 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + 39585 ( - 1 ) 3 / 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 39585 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 39585 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ 13 8 2 45 8 -1 z 1 983040 z 37 8 -1 1073 -1 1 8 -6825 1 -1 -1 3 8 z 1 8 z 3 6825 -1 3 8 z 1 8 1 z 3 -1 6825 -1 3 4 1 -1 -1 5 8 z 1 8 z 3 6825 -1 3 4 -1 5 8 z 1 8 1 z 3 6825 1 -1 -1 7 8 z 1 8 z 3 -1 6825 -1 7 8 z 1 8 1 z 3 47336 -1 7 8 z 21 8 -1 53235 1 -1 -1 3 8 z 1 8 z 2 53235 -1 3 8 z 1 8 1 z 2 -1 53235 -1 3 4 1 -1 -1 5 8 z 1 8 z 2 53235 -1 3 4 -1 5 8 z 1 8 1 z 2 53235 1 -1 -1 7 8 z 1 8 z 2 -1 53235 -1 7 8 z 1 8 1 z 2 113232 -1 7 8 z 13 8 -1 85995 1 -1 -1 3 8 z 1 8 z 85995 -1 3 8 z 1 8 1 z -1 85995 -1 3 4 1 -1 -1 5 8 z 1 8 z 85995 -1 3 4 -1 5 8 z 1 8 1 z 85995 1 -1 -1 7 8 z 1 8 z -1 85995 -1 7 8 z 1 8 1 z 63336 -1 7 8 z 5 8 1365 -1 1 4 z 1 2 5 z 29 1 -1 -1 1 8 z 1 8 -1 1365 -1 1 4 z 1 2 5 z 29 -1 1 8 z 1 8 1 -1 39585 1 -1 -1 3 8 z 1 8 39585 -1 3 8 z 1 8 1 -1 39585 -1 3 4 1 -1 -1 5 8 z 1 8 39585 -1 3 4 -1 5 8 z 1 8 1 39585 1 -1 -1 7 8 z 1 8 -1 39585 -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