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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(9/8), 5, 39/8, z] == (1/(68719476736 z^(31/8))) (4991 (-1)^(1/4) (8280 (-1)^(3/4) z^(7/8) + 20064 (-1)^(3/4) z^(15/8) + 46800 (-1)^(3/4) z^(23/8) - 13613600 (-1)^(3/4) z^(31/8) + 13800600 (-1)^(3/4) z^(39/8) + 45 (-1)^(3/4) (161 + 315 z + 714 z^2 + 2550 z^3 - 42075 z^4 + 38335 z^5) Log[1 - z^(1/8)] - 45 (-1)^(1/4) (161 + 315 z + 714 z^2 + 2550 z^3 - 42075 z^4 + 38335 z^5) Log[1 - I z^(1/8)] + 7245 (-1)^(1/4) Log[1 + I z^(1/8)] + 14175 (-1)^(1/4) z Log[1 + I z^(1/8)] + 32130 (-1)^(1/4) z^2 Log[1 + I z^(1/8)] + 114750 (-1)^(1/4) z^3 Log[1 + I z^(1/8)] - 1893375 (-1)^(1/4) z^4 Log[1 + I z^(1/8)] + 1725075 (-1)^(1/4) z^5 Log[1 + I z^(1/8)] - 7245 (-1)^(3/4) Log[1 + z^(1/8)] - 14175 (-1)^(3/4) z Log[1 + z^(1/8)] - 32130 (-1)^(3/4) z^2 Log[1 + z^(1/8)] - 114750 (-1)^(3/4) z^3 Log[1 + z^(1/8)] + 1893375 (-1)^(3/4) z^4 Log[1 + z^(1/8)] - 1725075 (-1)^(3/4) z^5 Log[1 + z^(1/8)] - 7245 Log[1 - (-1)^(1/4) z^(1/8)] - 14175 z Log[1 - (-1)^(1/4) z^(1/8)] - 32130 z^2 Log[1 - (-1)^(1/4) z^(1/8)] - 114750 z^3 Log[1 - (-1)^(1/4) z^(1/8)] + 1893375 z^4 Log[1 - (-1)^(1/4) z^(1/8)] - 1725075 z^5 Log[1 - (-1)^(1/4) z^(1/8)] + 7245 Log[1 + (-1)^(1/4) z^(1/8)] + 14175 z Log[1 + (-1)^(1/4) z^(1/8)] + 32130 z^2 Log[1 + (-1)^(1/4) z^(1/8)] + 114750 z^3 Log[1 + (-1)^(1/4) z^(1/8)] - 1893375 z^4 Log[1 + (-1)^(1/4) z^(1/8)] + 1725075 z^5 Log[1 + (-1)^(1/4) z^(1/8)] - 7245 I Log[1 - (-1)^(3/4) z^(1/8)] - 14175 I z Log[1 - (-1)^(3/4) z^(1/8)] - 32130 I z^2 Log[1 - (-1)^(3/4) z^(1/8)] - 114750 I z^3 Log[1 - (-1)^(3/4) z^(1/8)] + 1893375 I z^4 Log[1 - (-1)^(3/4) z^(1/8)] - 1725075 I z^5 Log[1 - (-1)^(3/4) z^(1/8)] + 7245 I Log[1 + (-1)^(3/4) z^(1/8)] + 14175 I z Log[1 + (-1)^(3/4) z^(1/8)] + 32130 I z^2 Log[1 + (-1)^(3/4) z^(1/8)] + 114750 I z^3 Log[1 + (-1)^(3/4) z^(1/8)] - 1893375 I z^4 Log[1 + (-1)^(3/4) z^(1/8)] + 1725075 I z^5 Log[1 + (-1)^(3/4) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 9 8 , 5 ; 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["5", 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["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 68719476736 z 31 / 8 ( 4991 - 1 4 ( 1725075 - 1 4 log ( z 8 + 1 ) z 5 - 1725075 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 5 - 1725075 log ( 1 - - 1 4 z 8 ) z 5 + 1725075 log ( - 1 4 z 8 + 1 ) z 5 - 1725075 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 5 + 1725075 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 5 + 13800600 ( - 1 ) 3 / 4 z 39 / 8 - 1893375 - 1 4 log ( z 8 + 1 ) z 4 + 1893375 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 4 + 1893375 log ( 1 - - 1 4 z 8 ) z 4 - 1893375 log ( - 1 4 z 8 + 1 ) z 4 + 1893375 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 4 - 1893375 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 4 - 13613600 ( - 1 ) 3 / 4 z 31 / 8 + 114750 - 1 4 log ( z 8 + 1 ) z 3 - 114750 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 3 - 114750 log ( 1 - - 1 4 z 8 ) z 3 + 114750 log ( - 1 4 z 8 + 1 ) z 3 - 114750 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 3 + 114750 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 3 + 46800 ( - 1 ) 3 / 4 z 23 / 8 + 32130 - 1 4 log ( z 8 + 1 ) z 2 - 32130 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 2 - 32130 log ( 1 - - 1 4 z 8 ) z 2 + 32130 log ( - 1 4 z 8 + 1 ) z 2 - 32130 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 2 + 32130 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 2 + 20064 ( - 1 ) 3 / 4 z 15 / 8 + 14175 - 1 4 log ( z 8 + 1 ) z - 14175 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z - 14175 log ( 1 - - 1 4 z 8 ) z + 14175 log ( - 1 4 z 8 + 1 ) z - 14175 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z + 14175 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z + 8280 ( - 1 ) 3 / 4 z 7 / 8 + 45 ( - 1 ) 3 / 4 ( 38335 z 5 - 42075 z 4 + 2550 z 3 + 714 z 2 + 315 z + 161 ) log ( 1 - z 8 ) - 45 - 1 4 ( 38335 z 5 - 42075 z 4 + 2550 z 3 + 714 z 2 + 315 z + 161 ) log ( 1 - z 8 ) + 7245 - 1 4 log ( z 8 + 1 ) - 7245 ( - 1 ) 3 / 4 log ( z 8 + 1 ) - 7245 log ( 1 - - 1 4 z 8 ) + 7245 log ( - 1 4 z 8 + 1 ) - 7245 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 7245 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) HypergeometricPFQ -1 9 8 5 39 8 z 1 68719476736 z 31 8 -1 4991 -1 1 4 1725075 -1 1 4 z 1 8 1 z 5 -1 1725075 -1 3 4 z 1 8 1 z 5 -1 1725075 1 -1 -1 1 4 z 1 8 z 5 1725075 -1 1 4 z 1 8 1 z 5 -1 1725075 1 -1 -1 3 4 z 1 8 z 5 1725075 -1 3 4 z 1 8 1 z 5 13800600 -1 3 4 z 39 8 -1 1893375 -1 1 4 z 1 8 1 z 4 1893375 -1 3 4 z 1 8 1 z 4 1893375 1 -1 -1 1 4 z 1 8 z 4 -1 1893375 -1 1 4 z 1 8 1 z 4 1893375 1 -1 -1 3 4 z 1 8 z 4 -1 1893375 -1 3 4 z 1 8 1 z 4 -1 13613600 -1 3 4 z 31 8 114750 -1 1 4 z 1 8 1 z 3 -1 114750 -1 3 4 z 1 8 1 z 3 -1 114750 1 -1 -1 1 4 z 1 8 z 3 114750 -1 1 4 z 1 8 1 z 3 -1 114750 1 -1 -1 3 4 z 1 8 z 3 114750 -1 3 4 z 1 8 1 z 3 46800 -1 3 4 z 23 8 32130 -1 1 4 z 1 8 1 z 2 -1 32130 -1 3 4 z 1 8 1 z 2 -1 32130 1 -1 -1 1 4 z 1 8 z 2 32130 -1 1 4 z 1 8 1 z 2 -1 32130 1 -1 -1 3 4 z 1 8 z 2 32130 -1 3 4 z 1 8 1 z 2 20064 -1 3 4 z 15 8 14175 -1 1 4 z 1 8 1 z -1 14175 -1 3 4 z 1 8 1 z -1 14175 1 -1 -1 1 4 z 1 8 z 14175 -1 1 4 z 1 8 1 z -1 14175 1 -1 -1 3 4 z 1 8 z 14175 -1 3 4 z 1 8 1 z 8280 -1 3 4 z 7 8 45 -1 3 4 38335 z 5 -1 42075 z 4 2550 z 3 714 z 2 315 z 161 1 -1 z 1 8 -1 45 -1 1 4 38335 z 5 -1 42075 z 4 2550 z 3 714 z 2 315 z 161 1 -1 z 1 8 7245 -1 1 4 z 1 8 1 -1 7245 -1 3 4 z 1 8 1 -1 7245 1 -1 -1 1 4 z 1 8 7245 -1 1 4 z 1 8 1 -1 7245 1 -1 -1 3 4 z 1 8 7245 -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