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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.btk2.01

 Input Form

 Hypergeometric2F1[-(7/8), 3, 41/8, z] == -((1/(268435456 z^(33/8))) (935 (-1)^(1/4) (-214200 (-1)^(3/4) z^(1/8) + 361760 (-1)^(3/4) z^(9/8) - 15120 (-1)^(3/4) z^(17/8) - 26208 (-1)^(3/4) z^(25/8) + 24840 (-1)^(3/4) z^(33/8) + 315 (-1)^(3/4) (-1 + z)^3 (85 + 102 z + 69 z^2) Log[1 - z^(1/8)] + 315 (-1)^(1/4) (-1 + z)^3 (85 + 102 z + 69 z^2) Log[1 - I z^(1/8)] + 26775 (-1)^(1/4) Log[1 + I z^(1/8)] - 48195 (-1)^(1/4) z Log[1 + I z^(1/8)] + 5670 (-1)^(1/4) z^2 Log[1 + I z^(1/8)] + 4410 (-1)^(1/4) z^3 Log[1 + I z^(1/8)] + 33075 (-1)^(1/4) z^4 Log[1 + I z^(1/8)] - 21735 (-1)^(1/4) z^5 Log[1 + I z^(1/8)] + 26775 (-1)^(3/4) Log[1 + z^(1/8)] - 48195 (-1)^(3/4) z Log[1 + z^(1/8)] + 5670 (-1)^(3/4) z^2 Log[1 + z^(1/8)] + 4410 (-1)^(3/4) z^3 Log[1 + z^(1/8)] + 33075 (-1)^(3/4) z^4 Log[1 + z^(1/8)] - 21735 (-1)^(3/4) z^5 Log[1 + z^(1/8)] - 26775 I Log[1 - (-1)^(1/4) z^(1/8)] + 48195 I z Log[1 - (-1)^(1/4) z^(1/8)] - 5670 I z^2 Log[1 - (-1)^(1/4) z^(1/8)] - 4410 I z^3 Log[1 - (-1)^(1/4) z^(1/8)] - 33075 I z^4 Log[1 - (-1)^(1/4) z^(1/8)] + 21735 I z^5 Log[1 - (-1)^(1/4) z^(1/8)] + 26775 I Log[1 + (-1)^(1/4) z^(1/8)] - 48195 I z Log[1 + (-1)^(1/4) z^(1/8)] + 5670 I z^2 Log[1 + (-1)^(1/4) z^(1/8)] + 4410 I z^3 Log[1 + (-1)^(1/4) z^(1/8)] + 33075 I z^4 Log[1 + (-1)^(1/4) z^(1/8)] - 21735 I z^5 Log[1 + (-1)^(1/4) z^(1/8)] - 26775 Log[1 - (-1)^(3/4) z^(1/8)] + 48195 z Log[1 - (-1)^(3/4) z^(1/8)] - 5670 z^2 Log[1 - (-1)^(3/4) z^(1/8)] - 4410 z^3 Log[1 - (-1)^(3/4) z^(1/8)] - 33075 z^4 Log[1 - (-1)^(3/4) z^(1/8)] + 21735 z^5 Log[1 - (-1)^(3/4) z^(1/8)] + 26775 Log[1 + (-1)^(3/4) z^(1/8)] - 48195 z Log[1 + (-1)^(3/4) z^(1/8)] + 5670 z^2 Log[1 + (-1)^(3/4) z^(1/8)] + 4410 z^3 Log[1 + (-1)^(3/4) z^(1/8)] + 33075 z^4 Log[1 + (-1)^(3/4) z^(1/8)] - 21735 z^5 Log[1 + (-1)^(3/4) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( - 7 8 , 3 ; 41 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["7", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["41", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["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 33 / 8 ( 935 - 1 4 ( - 21735 - 1 4 log ( z 8 + 1 ) z 5 - 21735 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 5 + 21735 log ( 1 - - 1 4 z 8 ) z 5 - 21735 log ( - 1 4 z 8 + 1 ) z 5 + 21735 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 5 - 21735 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 5 + 24840 ( - 1 ) 3 / 4 z 33 / 8 + 33075 - 1 4 log ( z 8 + 1 ) z 4 + 33075 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 4 - 33075 log ( 1 - - 1 4 z 8 ) z 4 + 33075 log ( - 1 4 z 8 + 1 ) z 4 - 33075 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 4 + 33075 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 4 - 26208 ( - 1 ) 3 / 4 z 25 / 8 + 4410 - 1 4 log ( z 8 + 1 ) z 3 + 4410 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 3 - 4410 log ( 1 - - 1 4 z 8 ) z 3 + 4410 log ( - 1 4 z 8 + 1 ) z 3 - 4410 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 3 + 4410 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 3 - 15120 ( - 1 ) 3 / 4 z 17 / 8 + 5670 - 1 4 log ( z 8 + 1 ) z 2 + 5670 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 2 - 5670 log ( 1 - - 1 4 z 8 ) z 2 + 5670 log ( - 1 4 z 8 + 1 ) z 2 - 5670 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 2 + 5670 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 2 + 361760 ( - 1 ) 3 / 4 z 9 / 8 - 48195 - 1 4 log ( z 8 + 1 ) z - 48195 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z + 48195 log ( 1 - - 1 4 z 8 ) z - 48195 log ( - 1 4 z 8 + 1 ) z + 48195 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z - 48195 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z - 214200 ( - 1 ) 3 / 4 z 8 + 315 ( - 1 ) 3 / 4 ( z - 1 ) 3 ( 69 z 2 + 102 z + 85 ) log ( 1 - z 8 ) + 315 - 1 4 ( z - 1 ) 3 ( 69 z 2 + 102 z + 85 ) log ( 1 - z 8 ) + 26775 - 1 4 log ( z 8 + 1 ) + 26775 ( - 1 ) 3 / 4 log ( z 8 + 1 ) - 26775 log ( 1 - - 1 4 z 8 ) + 26775 log ( - 1 4 z 8 + 1 ) - 26775 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 26775 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) HypergeometricPFQ -1 7 8 3 41 8 z -1 1 268435456 z 33 8 -1 935 -1 1 4 -21735 -1 1 4 z 1 8 1 z 5 -1 21735 -1 3 4 z 1 8 1 z 5 21735 1 -1 -1 1 4 z 1 8 z 5 -1 21735 -1 1 4 z 1 8 1 z 5 21735 1 -1 -1 3 4 z 1 8 z 5 -1 21735 -1 3 4 z 1 8 1 z 5 24840 -1 3 4 z 33 8 33075 -1 1 4 z 1 8 1 z 4 33075 -1 3 4 z 1 8 1 z 4 -1 33075 1 -1 -1 1 4 z 1 8 z 4 33075 -1 1 4 z 1 8 1 z 4 -1 33075 1 -1 -1 3 4 z 1 8 z 4 33075 -1 3 4 z 1 8 1 z 4 -1 26208 -1 3 4 z 25 8 4410 -1 1 4 z 1 8 1 z 3 4410 -1 3 4 z 1 8 1 z 3 -1 4410 1 -1 -1 1 4 z 1 8 z 3 4410 -1 1 4 z 1 8 1 z 3 -1 4410 1 -1 -1 3 4 z 1 8 z 3 4410 -1 3 4 z 1 8 1 z 3 -1 15120 -1 3 4 z 17 8 5670 -1 1 4 z 1 8 1 z 2 5670 -1 3 4 z 1 8 1 z 2 -1 5670 1 -1 -1 1 4 z 1 8 z 2 5670 -1 1 4 z 1 8 1 z 2 -1 5670 1 -1 -1 3 4 z 1 8 z 2 5670 -1 3 4 z 1 8 1 z 2 361760 -1 3 4 z 9 8 -1 48195 -1 1 4 z 1 8 1 z -1 48195 -1 3 4 z 1 8 1 z 48195 1 -1 -1 1 4 z 1 8 z -1 48195 -1 1 4 z 1 8 1 z 48195 1 -1 -1 3 4 z 1 8 z -1 48195 -1 3 4 z 1 8 1 z -1 214200 -1 3 4 z 1 8 315 -1 3 4 z -1 3 69 z 2 102 z 85 1 -1 z 1 8 315 -1 1 4 z -1 3 69 z 2 102 z 85 1 -1 z 1 8 26775 -1 1 4 z 1 8 1 26775 -1 3 4 z 1 8 1 -1 26775 1 -1 -1 1 4 z 1 8 26775 -1 1 4 z 1 8 1 -1 26775 1 -1 -1 3 4 z 1 8 26775 -1 3 4 z 1 8 1 [/itex]

 Rule Form

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

 2007-05-02