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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b72d.01

 Input Form

 Hypergeometric2F1[-(45/8), 4, 3/8, -z] == (1/2147483648) (4393935 ((-(2639/5)) (-8 - 5 (-1)^(5/8) z^(5/8) Log[1 - (-1)^(1/8) z^(1/8)] + 5 (-1)^(5/8) z^(5/8) Log[1 + (-1)^(1/8) z^(1/8)] + 5 (-1)^(7/8) z^(5/8) Log[1 - (-1)^(3/8) z^(1/8)] - 5 (-1)^(7/8) z^(5/8) Log[1 + (-1)^(3/8) z^(1/8)] + 5 (-1)^(1/8) z^(5/8) Log[1 - (-1)^(5/8) z^(1/8)] - 5 (-1)^(1/8) z^(5/8) Log[1 + (-1)^(5/8) z^(1/8)] - 5 (-1)^(3/8) z^(5/8) Log[1 - (-1)^(7/8) z^(1/8)] + 5 (-1)^(3/8) z^(5/8) Log[1 + (-1)^(7/8) z^(1/8)]) + 37555 (-(8/13) + (8 z)/5 + (-1)^(1/8) z^(13/8) (I Log[1 - (-1)^(1/8) z^(1/8)] - I Log[1 + (-1)^(1/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] - Log[1 - (-1)^(5/8) z^(1/8)] + Log[1 + (-1)^(5/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)])) + 294150 (-(8/29) + (8 z)/21 - (8 z^2)/13 + (8 z^3)/5 + (-1)^(1/8) z^(29/8) (I Log[1 - (-1)^(1/8) z^(1/8)] - I Log[1 + (-1)^(1/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] - Log[1 - (-1)^(5/8) z^(1/8)] + Log[1 + (-1)^(5/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)])) + 74359 (-(8/45) + (8 z)/37 - (8 z^2)/29 + (8 z^3)/21 - (8 z^4)/13 + (8 z^5)/5 + (-1)^(1/8) z^(45/8) (I Log[1 - (-1)^(1/8) z^(1/8)] - I Log[1 + (-1)^(1/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] - Log[1 - (-1)^(5/8) z^(1/8)] + Log[1 + (-1)^(5/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)])) - 160950 (-(8/21) + (8 z)/13 - (8 z^2)/5 + (-1)^(1/8) z^(21/8) ((-I) Log[1 - (-1)^(1/8) z^(1/8)] + I Log[1 + (-1)^(1/8) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] + Log[1 - (-1)^(5/8) z^(1/8)] - Log[1 + (-1)^(5/8) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)])) - 242475 (-(8/37) + (8 z)/29 - (8 z^2)/21 + (8 z^3)/13 - (8 z^4)/5 + (-1)^(1/8) z^(37/8) ((-I) Log[1 - (-1)^(1/8) z^(1/8)] + I Log[1 + (-1)^(1/8) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] + Log[1 - (-1)^(5/8) z^(1/8)] - Log[1 + (-1)^(5/8) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 45 8 , 4 ; 3 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["45", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["3", "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 2147483648 ( 4393935 ( - 2639 5 ( - 5 ( - 1 ) 5 / 8 z 5 / 8 log ( 1 - - 1 8 z 8 ) + 5 ( - 1 ) 5 / 8 z 5 / 8 log ( - 1 8 z 8 + 1 ) + 5 ( - 1 ) 7 / 8 z 5 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 5 ( - 1 ) 7 / 8 z 5 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 5 - 1 8 z 5 / 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 5 - 1 8 z 5 / 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 5 ( - 1 ) 3 / 8 z 5 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 5 ( - 1 ) 3 / 8 z 5 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) - 8 ) + 37555 ( - 1 8 ( log ( 1 - - 1 8 z 8 ) - log ( - 1 8 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 5 / 8 z 8 ) + log ( ( - 1 ) 5 / 8 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 13 / 8 + 8 z 5 - 8 13 ) + 294150 ( - 1 8 ( log ( 1 - - 1 8 z 8 ) - log ( - 1 8 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 5 / 8 z 8 ) + log ( ( - 1 ) 5 / 8 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 29 / 8 + 8 z 3 5 - 8 z 2 13 + 8 z 21 - 8 29 ) + 74359 ( - 1 8 ( log ( 1 - - 1 8 z 8 ) - log ( - 1 8 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 5 / 8 z 8 ) + log ( ( - 1 ) 5 / 8 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 45 / 8 + 8 z 5 5 - 8 z 4 13 + 8 z 3 21 - 8 z 2 29 + 8 z 37 - 8 45 ) - 160950 ( - 1 8 ( - log ( 1 - - 1 8 z 8 ) + log ( - 1 8 z 8 + 1 ) + ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 5 / 8 z 8 ) - log ( ( - 1 ) 5 / 8 z 8 + 1 ) - - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 21 / 8 - 8 z 2 5 + 8 z 13 - 8 21 ) - 242475 ( - 1 8 ( - log ( 1 - - 1 8 z 8 ) + log ( - 1 8 z 8 + 1 ) + ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 5 / 8 z 8 ) - log ( ( - 1 ) 5 / 8 z 8 + 1 ) - - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 37 / 8 - 8 z 4 5 + 8 z 3 13 - 8 z 2 21 + 8 z 29 - 8 37 ) ) ) HypergeometricPFQ -1 45 8 4 3 8 -1 z 1 2147483648 4393935 -1 2639 5 -5 -1 5 8 z 5 8 1 -1 -1 1 8 z 1 8 5 -1 5 8 z 5 8 -1 1 8 z 1 8 1 5 -1 7 8 z 5 8 1 -1 -1 3 8 z 1 8 -1 5 -1 7 8 z 5 8 -1 3 8 z 1 8 1 5 -1 1 8 z 5 8 1 -1 -1 5 8 z 1 8 -1 5 -1 1 8 z 5 8 -1 5 8 z 1 8 1 -1 5 -1 3 8 z 5 8 1 -1 -1 7 8 z 1 8 5 -1 3 8 z 5 8 -1 7 8 z 1 8 1 -8 37555 -1 1 8 1 -1 -1 1 8 z 1 8 -1 -1 1 8 z 1 8 1 -1 -1 3 4 1 -1 -1 3 8 z 1 8 -1 3 4 -1 3 8 z 1 8 1 -1 1 -1 -1 5 8 z 1 8 -1 5 8 z 1 8 1 -1 1 4 1 -1 -1 7 8 z 1 8 -1 -1 1 4 -1 7 8 z 1 8 1 z 13 8 8 z 5 -1 -1 8 13 294150 -1 1 8 1 -1 -1 1 8 z 1 8 -1 -1 1 8 z 1 8 1 -1 -1 3 4 1 -1 -1 3 8 z 1 8 -1 3 4 -1 3 8 z 1 8 1 -1 1 -1 -1 5 8 z 1 8 -1 5 8 z 1 8 1 -1 1 4 1 -1 -1 7 8 z 1 8 -1 -1 1 4 -1 7 8 z 1 8 1 z 29 8 8 z 3 5 -1 -1 8 z 2 13 -1 8 z 21 -1 -1 8 29 74359 -1 1 8 1 -1 -1 1 8 z 1 8 -1 -1 1 8 z 1 8 1 -1 -1 3 4 1 -1 -1 3 8 z 1 8 -1 3 4 -1 3 8 z 1 8 1 -1 1 -1 -1 5 8 z 1 8 -1 5 8 z 1 8 1 -1 1 4 1 -1 -1 7 8 z 1 8 -1 -1 1 4 -1 7 8 z 1 8 1 z 45 8 8 z 5 5 -1 -1 8 z 4 13 -1 8 z 3 21 -1 -1 8 z 2 29 -1 8 z 37 -1 -1 8 45 -1 160950 -1 1 8 -1 1 -1 -1 1 8 z 1 8 -1 1 8 z 1 8 1 -1 3 4 1 -1 -1 3 8 z 1 8 -1 -1 3 4 -1 3 8 z 1 8 1 1 -1 -1 5 8 z 1 8 -1 -1 5 8 z 1 8 1 -1 -1 1 4 1 -1 -1 7 8 z 1 8 -1 1 4 -1 7 8 z 1 8 1 z 21 8 -1 8 z 2 5 -1 8 z 13 -1 -1 8 21 -1 242475 -1 1 8 -1 1 -1 -1 1 8 z 1 8 -1 1 8 z 1 8 1 -1 3 4 1 -1 -1 3 8 z 1 8 -1 -1 3 4 -1 3 8 z 1 8 1 1 -1 -1 5 8 z 1 8 -1 -1 5 8 z 1 8 1 -1 -1 1 4 1 -1 -1 7 8 z 1 8 -1 1 4 -1 7 8 z 1 8 1 z 37 8 -1 8 z 4 5 -1 8 z 3 13 -1 -1 8 z 2 21 -1 8 z 29 -1 -1 8 37 [/itex]

 Rule Form

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

 2007-05-02