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.by33.01

 Input Form

 Hypergeometric2F1[1/8, 5, 33/8, -z] == -((1/(268435456 z^(25/8) (1 + z))) (425 (-1)^(1/8) (8568 (-1)^(7/8) z^(1/8) - 15064 (-1)^(7/8) z^(9/8) + 37352 (-1)^(7/8) z^(17/8) + 85560 (-1)^(7/8) z^(25/8) - 21 (-1)^(3/4) (-51 + 84 z - 210 z^2 + 3220 z^3 + 3565 z^4) Log[1 - (-1)^(1/8) z^(1/8)] + 21 (-1)^(3/4) (-51 + 84 z - 210 z^2 + 3220 z^3 + 3565 z^4) Log[1 + (-1)^(1/8) z^(1/8)] + 1071 I Log[1 - (-1)^(3/8) z^(1/8)] - 1764 I z Log[1 - (-1)^(3/8) z^(1/8)] + 4410 I z^2 Log[1 - (-1)^(3/8) z^(1/8)] - 67620 I z^3 Log[1 - (-1)^(3/8) z^(1/8)] - 74865 I z^4 Log[1 - (-1)^(3/8) z^(1/8)] - 1071 I Log[1 + (-1)^(3/8) z^(1/8)] + 1764 I z Log[1 + (-1)^(3/8) z^(1/8)] - 4410 I z^2 Log[1 + (-1)^(3/8) z^(1/8)] + 67620 I z^3 Log[1 + (-1)^(3/8) z^(1/8)] + 74865 I z^4 Log[1 + (-1)^(3/8) z^(1/8)] + 1071 (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] - 1764 (-1)^(1/4) z Log[1 - (-1)^(5/8) z^(1/8)] + 4410 (-1)^(1/4) z^2 Log[1 - (-1)^(5/8) z^(1/8)] - 67620 (-1)^(1/4) z^3 Log[1 - (-1)^(5/8) z^(1/8)] - 74865 (-1)^(1/4) z^4 Log[1 - (-1)^(5/8) z^(1/8)] - 1071 (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] + 1764 (-1)^(1/4) z Log[1 + (-1)^(5/8) z^(1/8)] - 4410 (-1)^(1/4) z^2 Log[1 + (-1)^(5/8) z^(1/8)] + 67620 (-1)^(1/4) z^3 Log[1 + (-1)^(5/8) z^(1/8)] + 74865 (-1)^(1/4) z^4 Log[1 + (-1)^(5/8) z^(1/8)] + 1071 Log[1 - (-1)^(7/8) z^(1/8)] - 1764 z Log[1 - (-1)^(7/8) z^(1/8)] + 4410 z^2 Log[1 - (-1)^(7/8) z^(1/8)] - 67620 z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 74865 z^4 Log[1 - (-1)^(7/8) z^(1/8)] - 1071 Log[1 + (-1)^(7/8) z^(1/8)] + 1764 z Log[1 + (-1)^(7/8) z^(1/8)] - 4410 z^2 Log[1 + (-1)^(7/8) z^(1/8)] + 67620 z^3 Log[1 + (-1)^(7/8) z^(1/8)] + 74865 z^4 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( 1 8 , 5 ; 33 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["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["33", "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 268435456 z 25 / 8 ( z + 1 ) ( 425 - 1 8 ( - 74865 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 4 + 74865 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 4 - 74865 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 4 + 74865 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 4 - 74865 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 4 + 74865 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 4 + 85560 ( - 1 ) 7 / 8 z 25 / 8 - 67620 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 3 + 67620 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 3 - 67620 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 3 + 67620 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 3 - 67620 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 3 + 67620 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 3 + 37352 ( - 1 ) 7 / 8 z 17 / 8 + 4410 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 - 4410 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 + 4410 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 - 4410 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 + 4410 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 - 4410 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 - 15064 ( - 1 ) 7 / 8 z 9 / 8 - 1764 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z + 1764 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z - 1764 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z + 1764 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z - 1764 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z + 1764 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 8568 ( - 1 ) 7 / 8 z 8 - 21 ( - 1 ) 3 / 4 ( 3565 z 4 + 3220 z 3 - 210 z 2 + 84 z - 51 ) log ( 1 - - 1 8 z 8 ) + 21 ( - 1 ) 3 / 4 ( 3565 z 4 + 3220 z 3 - 210 z 2 + 84 z - 51 ) log ( - 1 8 z 8 + 1 ) + 1071 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 1071 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 1071 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 1071 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 1071 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 1071 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ 1 8 5 33 8 -1 z -1 1 268435456 z 25 8 z 1 -1 425 -1 1 8 -74865 1 -1 -1 3 8 z 1 8 z 4 74865 -1 3 8 z 1 8 1 z 4 -1 74865 -1 1 4 1 -1 -1 5 8 z 1 8 z 4 74865 -1 1 4 -1 5 8 z 1 8 1 z 4 -1 74865 1 -1 -1 7 8 z 1 8 z 4 74865 -1 7 8 z 1 8 1 z 4 85560 -1 7 8 z 25 8 -1 67620 1 -1 -1 3 8 z 1 8 z 3 67620 -1 3 8 z 1 8 1 z 3 -1 67620 -1 1 4 1 -1 -1 5 8 z 1 8 z 3 67620 -1 1 4 -1 5 8 z 1 8 1 z 3 -1 67620 1 -1 -1 7 8 z 1 8 z 3 67620 -1 7 8 z 1 8 1 z 3 37352 -1 7 8 z 17 8 4410 1 -1 -1 3 8 z 1 8 z 2 -1 4410 -1 3 8 z 1 8 1 z 2 4410 -1 1 4 1 -1 -1 5 8 z 1 8 z 2 -1 4410 -1 1 4 -1 5 8 z 1 8 1 z 2 4410 1 -1 -1 7 8 z 1 8 z 2 -1 4410 -1 7 8 z 1 8 1 z 2 -1 15064 -1 7 8 z 9 8 -1 1764 1 -1 -1 3 8 z 1 8 z 1764 -1 3 8 z 1 8 1 z -1 1764 -1 1 4 1 -1 -1 5 8 z 1 8 z 1764 -1 1 4 -1 5 8 z 1 8 1 z -1 1764 1 -1 -1 7 8 z 1 8 z 1764 -1 7 8 z 1 8 1 z 8568 -1 7 8 z 1 8 -1 21 -1 3 4 3565 z 4 3220 z 3 -1 210 z 2 84 z -51 1 -1 -1 1 8 z 1 8 21 -1 3 4 3565 z 4 3220 z 3 -1 210 z 2 84 z -51 -1 1 8 z 1 8 1 1071 1 -1 -1 3 8 z 1 8 -1 1071 -1 3 8 z 1 8 1 1071 -1 1 4 1 -1 -1 5 8 z 1 8 -1 1071 -1 1 4 -1 5 8 z 1 8 1 1071 1 -1 -1 7 8 z 1 8 -1 1071 -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