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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(9/8), 3, 39/8, -z] == -((1/(268435456 z^(31/8))) (713 (-1)^(1/8) (-24840 (-1)^(7/8) z^(7/8) - 26208 (-1)^(7/8) z^(15/8) + 15120 (-1)^(7/8) z^(23/8) + 361760 (-1)^(7/8) z^(31/8) + 214200 (-1)^(7/8) z^(39/8) - 315 (1 + z)^3 (69 - 102 z + 85 z^2) Log[1 - (-1)^(1/8) z^(1/8)] + 315 (1 + z)^3 (69 - 102 z + 85 z^2) Log[1 + (-1)^(1/8) z^(1/8)] - 21735 (-1)^(1/4) Log[1 - (-1)^(3/8) z^(1/8)] - 33075 (-1)^(1/4) z Log[1 - (-1)^(3/8) z^(1/8)] + 4410 (-1)^(1/4) z^2 Log[1 - (-1)^(3/8) z^(1/8)] - 5670 (-1)^(1/4) z^3 Log[1 - (-1)^(3/8) z^(1/8)] - 48195 (-1)^(1/4) z^4 Log[1 - (-1)^(3/8) z^(1/8)] - 26775 (-1)^(1/4) z^5 Log[1 - (-1)^(3/8) z^(1/8)] + 21735 (-1)^(1/4) Log[1 + (-1)^(3/8) z^(1/8)] + 33075 (-1)^(1/4) z Log[1 + (-1)^(3/8) z^(1/8)] - 4410 (-1)^(1/4) z^2 Log[1 + (-1)^(3/8) z^(1/8)] + 5670 (-1)^(1/4) z^3 Log[1 + (-1)^(3/8) z^(1/8)] + 48195 (-1)^(1/4) z^4 Log[1 + (-1)^(3/8) z^(1/8)] + 26775 (-1)^(1/4) z^5 Log[1 + (-1)^(3/8) z^(1/8)] - 21735 I Log[1 - (-1)^(5/8) z^(1/8)] - 33075 I z Log[1 - (-1)^(5/8) z^(1/8)] + 4410 I z^2 Log[1 - (-1)^(5/8) z^(1/8)] - 5670 I z^3 Log[1 - (-1)^(5/8) z^(1/8)] - 48195 I z^4 Log[1 - (-1)^(5/8) z^(1/8)] - 26775 I z^5 Log[1 - (-1)^(5/8) z^(1/8)] + 21735 I Log[1 + (-1)^(5/8) z^(1/8)] + 33075 I z Log[1 + (-1)^(5/8) z^(1/8)] - 4410 I z^2 Log[1 + (-1)^(5/8) z^(1/8)] + 5670 I z^3 Log[1 + (-1)^(5/8) z^(1/8)] + 48195 I z^4 Log[1 + (-1)^(5/8) z^(1/8)] + 26775 I z^5 Log[1 + (-1)^(5/8) z^(1/8)] - 21735 (-1)^(3/4) Log[1 - (-1)^(7/8) z^(1/8)] - 33075 (-1)^(3/4) z Log[1 - (-1)^(7/8) z^(1/8)] + 4410 (-1)^(3/4) z^2 Log[1 - (-1)^(7/8) z^(1/8)] - 5670 (-1)^(3/4) z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 48195 (-1)^(3/4) z^4 Log[1 - (-1)^(7/8) z^(1/8)] - 26775 (-1)^(3/4) z^5 Log[1 - (-1)^(7/8) z^(1/8)] + 21735 (-1)^(3/4) Log[1 + (-1)^(7/8) z^(1/8)] + 33075 (-1)^(3/4) z Log[1 + (-1)^(7/8) z^(1/8)] - 4410 (-1)^(3/4) z^2 Log[1 + (-1)^(7/8) z^(1/8)] + 5670 (-1)^(3/4) z^3 Log[1 + (-1)^(7/8) z^(1/8)] + 48195 (-1)^(3/4) z^4 Log[1 + (-1)^(7/8) z^(1/8)] + 26775 (-1)^(3/4) z^5 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( - 9 8 , 3 ; 39 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["9", "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["39", "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 31 / 8 ( 713 - 1 8 ( - 26775 - 1 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 5 + 26775 - 1 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 5 - 26775 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 5 + 26775 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 5 - 26775 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 5 + 26775 ( - 1 ) 3 / 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 5 + 214200 ( - 1 ) 7 / 8 z 39 / 8 - 48195 - 1 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 4 + 48195 - 1 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 4 - 48195 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 4 + 48195 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 4 - 48195 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 4 + 48195 ( - 1 ) 3 / 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 4 + 361760 ( - 1 ) 7 / 8 z 31 / 8 - 5670 - 1 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 3 + 5670 - 1 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 3 - 5670 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 3 + 5670 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 3 - 5670 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 3 + 5670 ( - 1 ) 3 / 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 3 + 15120 ( - 1 ) 7 / 8 z 23 / 8 + 4410 - 1 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 - 4410 - 1 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 + 4410 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 - 4410 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 + 4410 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 - 4410 ( - 1 ) 3 / 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 - 26208 ( - 1 ) 7 / 8 z 15 / 8 - 33075 - 1 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z + 33075 - 1 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z - 33075 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z + 33075 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z - 33075 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z + 33075 ( - 1 ) 3 / 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z - 24840 ( - 1 ) 7 / 8 z 7 / 8 - 315 ( z + 1 ) 3 ( 85 z 2 - 102 z + 69 ) log ( 1 - - 1 8 z 8 ) + 315 ( z + 1 ) 3 ( 85 z 2 - 102 z + 69 ) log ( - 1 8 z 8 + 1 ) - 21735 - 1 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + 21735 - 1 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - 21735 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + 21735 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 21735 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 21735 ( - 1 ) 3 / 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ -1 9 8 3 39 8 -1 z -1 1 268435456 z 31 8 -1 713 -1 1 8 -26775 -1 1 4 1 -1 -1 3 8 z 1 8 z 5 26775 -1 1 4 -1 3 8 z 1 8 1 z 5 -1 26775 1 -1 -1 5 8 z 1 8 z 5 26775 -1 5 8 z 1 8 1 z 5 -1 26775 -1 3 4 1 -1 -1 7 8 z 1 8 z 5 26775 -1 3 4 -1 7 8 z 1 8 1 z 5 214200 -1 7 8 z 39 8 -1 48195 -1 1 4 1 -1 -1 3 8 z 1 8 z 4 48195 -1 1 4 -1 3 8 z 1 8 1 z 4 -1 48195 1 -1 -1 5 8 z 1 8 z 4 48195 -1 5 8 z 1 8 1 z 4 -1 48195 -1 3 4 1 -1 -1 7 8 z 1 8 z 4 48195 -1 3 4 -1 7 8 z 1 8 1 z 4 361760 -1 7 8 z 31 8 -1 5670 -1 1 4 1 -1 -1 3 8 z 1 8 z 3 5670 -1 1 4 -1 3 8 z 1 8 1 z 3 -1 5670 1 -1 -1 5 8 z 1 8 z 3 5670 -1 5 8 z 1 8 1 z 3 -1 5670 -1 3 4 1 -1 -1 7 8 z 1 8 z 3 5670 -1 3 4 -1 7 8 z 1 8 1 z 3 15120 -1 7 8 z 23 8 4410 -1 1 4 1 -1 -1 3 8 z 1 8 z 2 -1 4410 -1 1 4 -1 3 8 z 1 8 1 z 2 4410 1 -1 -1 5 8 z 1 8 z 2 -1 4410 -1 5 8 z 1 8 1 z 2 4410 -1 3 4 1 -1 -1 7 8 z 1 8 z 2 -1 4410 -1 3 4 -1 7 8 z 1 8 1 z 2 -1 26208 -1 7 8 z 15 8 -1 33075 -1 1 4 1 -1 -1 3 8 z 1 8 z 33075 -1 1 4 -1 3 8 z 1 8 1 z -1 33075 1 -1 -1 5 8 z 1 8 z 33075 -1 5 8 z 1 8 1 z -1 33075 -1 3 4 1 -1 -1 7 8 z 1 8 z 33075 -1 3 4 -1 7 8 z 1 8 1 z -1 24840 -1 7 8 z 7 8 -1 315 z 1 3 85 z 2 -1 102 z 69 1 -1 -1 1 8 z 1 8 315 z 1 3 85 z 2 -1 102 z 69 -1 1 8 z 1 8 1 -1 21735 -1 1 4 1 -1 -1 3 8 z 1 8 21735 -1 1 4 -1 3 8 z 1 8 1 -1 21735 1 -1 -1 5 8 z 1 8 21735 -1 5 8 z 1 8 1 -1 21735 -1 3 4 1 -1 -1 7 8 z 1 8 21735 -1 3 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