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http://functions.wolfram.com/07.23.03.b880.01
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Hypergeometric2F1[-(43/8), 5, -(3/8), -z] ==
(1/8589934592) (2830905 (-257355 (-(8/11) + (8 z)/3 +
(-1)^(1/8) z^(11/8) ((-1)^(1/4) Log[1 - (-1)^(1/8) z^(1/8)] -
(-1)^(1/4) Log[1 + (-1)^(1/8) z^(1/8)] -
Log[1 - (-1)^(3/8) z^(1/8)] + Log[1 + (-1)^(3/8) z^(1/8)] -
(-1)^(3/4) Log[1 - (-1)^(5/8) z^(1/8)] + (-1)^(3/4)
Log[1 + (-1)^(5/8) z^(1/8)] + I Log[1 - (-1)^(7/8) z^(1/8)] -
I Log[1 + (-1)^(7/8) z^(1/8)])) -
9057090 (-(8/27) + (8 z)/19 - (8 z^2)/11 + (8 z^3)/3 +
(-1)^(1/8) z^(27/8) ((-1)^(1/4) Log[1 - (-1)^(1/8) z^(1/8)] -
(-1)^(1/4) Log[1 + (-1)^(1/8) z^(1/8)] -
Log[1 - (-1)^(3/8) z^(1/8)] + Log[1 + (-1)^(3/8) z^(1/8)] -
(-1)^(3/4) Log[1 - (-1)^(5/8) z^(1/8)] + (-1)^(3/4)
Log[1 + (-1)^(5/8) z^(1/8)] + I Log[1 - (-1)^(7/8) z^(1/8)] -
I Log[1 + (-1)^(7/8) z^(1/8)])) -
5040075 (-(8/43) + (8 z)/35 - (8 z^2)/27 + (8 z^3)/19 - (8 z^4)/11 +
(8 z^5)/3 + (-1)^(1/8) z^(43/8)
((-1)^(1/4) Log[1 - (-1)^(1/8) z^(1/8)] - (-1)^(1/4)
Log[1 + (-1)^(1/8) z^(1/8)] - Log[1 - (-1)^(3/8) z^(1/8)] +
Log[1 + (-1)^(3/8) z^(1/8)] - (-1)^(3/4)
Log[1 - (-1)^(5/8) z^(1/8)] + (-1)^(3/4)
Log[1 + (-1)^(5/8) z^(1/8)] + I Log[1 - (-1)^(7/8) z^(1/8)] -
I Log[1 + (-1)^(7/8) z^(1/8)])) +
2763180 (-(8/19) + (8 z)/11 - (8 z^2)/3 + (-1)^(1/8) z^(19/8)
((-(-1)^(1/4)) Log[1 - (-1)^(1/8) z^(1/8)] +
(-1)^(1/4) Log[1 + (-1)^(1/8) z^(1/8)] +
Log[1 - (-1)^(3/8) z^(1/8)] - Log[1 + (-1)^(3/8) z^(1/8)] +
(-1)^(3/4) Log[1 - (-1)^(5/8) z^(1/8)] - (-1)^(3/4)
Log[1 + (-1)^(5/8) z^(1/8)] - I Log[1 - (-1)^(7/8) z^(1/8)] +
I Log[1 + (-1)^(7/8) z^(1/8)])) +
11558572 (-(8/35) + (8 z)/27 - (8 z^2)/19 + (8 z^3)/11 - (8 z^4)/3 +
(-1)^(1/8) z^(35/8) ((-(-1)^(1/4)) Log[1 - (-1)^(1/8) z^(1/8)] +
(-1)^(1/4) Log[1 + (-1)^(1/8) z^(1/8)] +
Log[1 - (-1)^(3/8) z^(1/8)] - Log[1 + (-1)^(3/8) z^(1/8)] +
(-1)^(3/4) Log[1 - (-1)^(5/8) z^(1/8)] - (-1)^(3/4)
Log[1 + (-1)^(5/8) z^(1/8)] - I Log[1 - (-1)^(7/8) z^(1/8)] +
I Log[1 + (-1)^(7/8) z^(1/8)]))))
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 43 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 5 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 3 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> 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["43", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", HypergeometricPFQ, Rule[Editable, 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<mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mn> 3 </mn> </mfrac> <mo> - </mo> <mfrac> <mn> 8 </mn> <mn> 11 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 9057090 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 27 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mn> 3 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mn> 11 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mn> 19 </mn> </mfrac> <mo> - </mo> <mfrac> <mn> 8 </mn> <mn> 27 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 5040075 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 43 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mn> 3 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mn> 11 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mn> 19 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mn> 27 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mn> 35 </mn> </mfrac> <mo> - </mo> <mfrac> <mn> 8 </mn> <mn> 43 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2763180 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 19 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mn> 3 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mn> 11 </mn> </mfrac> <mo> - </mo> <mfrac> <mn> 8 </mn> <mn> 19 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 11558572 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 35 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mn> 3 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mn> 11 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mn> 19 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mn> 27 </mn> </mfrac> <mo> - </mo> <mfrac> <mn> 8 </mn> <mn> 35 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 43 <sep /> 8 </cn> </apply> <cn type='integer'> 5 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 8 </cn> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8589934592 </cn> <apply> <times /> <cn type='integer'> 2830905 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -257355 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> 1 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HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] | |
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