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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[3/8, 5, 43/8, -z] == -((1/(8589934592 z^(35/8))) (65835 (-1)^(1/8) (-45144 (-1)^(7/8) z^(3/8) + 45752 (-1)^(7/8) z^(11/8) - 50568 (-1)^(7/8) z^(19/8) + 63336 (-1)^(7/8) z^(27/8) - 3 I (5643 - 4180 z + 4290 z^2 - 5460 z^3 + 13195 z^4) Log[1 - (-1)^(1/8) z^(1/8)] + 3 I (5643 - 4180 z + 4290 z^2 - 5460 z^3 + 13195 z^4) Log[1 + (-1)^(1/8) z^(1/8)] + 16929 (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] - 12540 (-1)^(3/4) z Log[1 - (-1)^(3/8) z^(1/8)] + 12870 (-1)^(3/4) z^2 Log[1 - (-1)^(3/8) z^(1/8)] - 16380 (-1)^(3/4) z^3 Log[1 - (-1)^(3/8) z^(1/8)] + 39585 (-1)^(3/4) z^4 Log[1 - (-1)^(3/8) z^(1/8)] - 16929 (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] + 12540 (-1)^(3/4) z Log[1 + (-1)^(3/8) z^(1/8)] - 12870 (-1)^(3/4) z^2 Log[1 + (-1)^(3/8) z^(1/8)] + 16380 (-1)^(3/4) z^3 Log[1 + (-1)^(3/8) z^(1/8)] - 39585 (-1)^(3/4) z^4 Log[1 + (-1)^(3/8) z^(1/8)] + 16929 Log[1 - (-1)^(5/8) z^(1/8)] - 12540 z Log[1 - (-1)^(5/8) z^(1/8)] + 12870 z^2 Log[1 - (-1)^(5/8) z^(1/8)] - 16380 z^3 Log[1 - (-1)^(5/8) z^(1/8)] + 39585 z^4 Log[1 - (-1)^(5/8) z^(1/8)] - 16929 Log[1 + (-1)^(5/8) z^(1/8)] + 12540 z Log[1 + (-1)^(5/8) z^(1/8)] - 12870 z^2 Log[1 + (-1)^(5/8) z^(1/8)] + 16380 z^3 Log[1 + (-1)^(5/8) z^(1/8)] - 39585 z^4 Log[1 + (-1)^(5/8) z^(1/8)] - 16929 (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] + 12540 (-1)^(1/4) z Log[1 - (-1)^(7/8) z^(1/8)] - 12870 (-1)^(1/4) z^2 Log[1 - (-1)^(7/8) z^(1/8)] + 16380 (-1)^(1/4) z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 39585 (-1)^(1/4) z^4 Log[1 - (-1)^(7/8) z^(1/8)] + 16929 (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)] - 12540 (-1)^(1/4) z Log[1 + (-1)^(7/8) z^(1/8)] + 12870 (-1)^(1/4) z^2 Log[1 + (-1)^(7/8) z^(1/8)] - 16380 (-1)^(1/4) z^3 Log[1 + (-1)^(7/8) z^(1/8)] + 39585 (-1)^(1/4) z^4 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( 3 8 , 5 ; 43 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["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["43", "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 8589934592 z 35 / 8 ( 65835 - 1 8 ( 39585 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 4 - 39585 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 4 + 39585 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 4 - 39585 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 4 - 39585 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 4 + 39585 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 4 + 63336 ( - 1 ) 7 / 8 z 27 / 8 - 16380 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 3 + 16380 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 3 - 16380 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 3 + 16380 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 3 + 16380 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 3 - 16380 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 3 - 50568 ( - 1 ) 7 / 8 z 19 / 8 + 12870 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 - 12870 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 + 12870 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 - 12870 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 - 12870 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 + 12870 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 45752 ( - 1 ) 7 / 8 z 11 / 8 - 12540 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z + 12540 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z - 12540 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z + 12540 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z + 12540 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z - 12540 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z - 45144 ( - 1 ) 7 / 8 z 3 / 8 - 3 ( 13195 z 4 - 5460 z 3 + 4290 z 2 - 4180 z + 5643 ) log ( 1 - - 1 8 z 8 ) + 3 ( 13195 z 4 - 5460 z 3 + 4290 z 2 - 4180 z + 5643 ) log ( - 1 8 z 8 + 1 ) + 16929 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 16929 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 16929 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 16929 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 16929 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 16929 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ 3 8 5 43 8 -1 z -1 1 8589934592 z 35 8 -1 65835 -1 1 8 39585 -1 3 4 1 -1 -1 3 8 z 1 8 z 4 -1 39585 -1 3 4 -1 3 8 z 1 8 1 z 4 39585 1 -1 -1 5 8 z 1 8 z 4 -1 39585 -1 5 8 z 1 8 1 z 4 -1 39585 -1 1 4 1 -1 -1 7 8 z 1 8 z 4 39585 -1 1 4 -1 7 8 z 1 8 1 z 4 63336 -1 7 8 z 27 8 -1 16380 -1 3 4 1 -1 -1 3 8 z 1 8 z 3 16380 -1 3 4 -1 3 8 z 1 8 1 z 3 -1 16380 1 -1 -1 5 8 z 1 8 z 3 16380 -1 5 8 z 1 8 1 z 3 16380 -1 1 4 1 -1 -1 7 8 z 1 8 z 3 -1 16380 -1 1 4 -1 7 8 z 1 8 1 z 3 -1 50568 -1 7 8 z 19 8 12870 -1 3 4 1 -1 -1 3 8 z 1 8 z 2 -1 12870 -1 3 4 -1 3 8 z 1 8 1 z 2 12870 1 -1 -1 5 8 z 1 8 z 2 -1 12870 -1 5 8 z 1 8 1 z 2 -1 12870 -1 1 4 1 -1 -1 7 8 z 1 8 z 2 12870 -1 1 4 -1 7 8 z 1 8 1 z 2 45752 -1 7 8 z 11 8 -1 12540 -1 3 4 1 -1 -1 3 8 z 1 8 z 12540 -1 3 4 -1 3 8 z 1 8 1 z -1 12540 1 -1 -1 5 8 z 1 8 z 12540 -1 5 8 z 1 8 1 z 12540 -1 1 4 1 -1 -1 7 8 z 1 8 z -1 12540 -1 1 4 -1 7 8 z 1 8 1 z -1 45144 -1 7 8 z 3 8 -1 3 13195 z 4 -1 5460 z 3 4290 z 2 -1 4180 z 5643 1 -1 -1 1 8 z 1 8 3 13195 z 4 -1 5460 z 3 4290 z 2 -1 4180 z 5643 -1 1 8 z 1 8 1 16929 -1 3 4 1 -1 -1 3 8 z 1 8 -1 16929 -1 3 4 -1 3 8 z 1 8 1 16929 1 -1 -1 5 8 z 1 8 -1 16929 -1 5 8 z 1 8 1 -1 16929 -1 1 4 1 -1 -1 7 8 z 1 8 16929 -1 1 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