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http://functions.wolfram.com/03.20.06.0052.01
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KelvinKer[\[Nu], z] \[Proportional]
(-(E^(-(((1 + I) z)/Sqrt[2]) + (I Pi \[Nu])/2)/
(8 Sqrt[2 Pi] Sqrt[(-(-1)^(1/4)) z] ((-1)^(3/4) z)^(3/2))))
((Sqrt[(-(-1)^(1/4)) z] (Pi (4 (-1)^\[Nu] z - 3 I E^((1 + I) Sqrt[2] z)
z + ((3 - 3 I) (-1)^\[Nu] Sqrt[I z^2])/Sqrt[2]) +
4 (E^((1 + I) Sqrt[2] z) z + (-1)^(1/4 + \[Nu]) Sqrt[I z^2])
(-Log[z] + Log[(-1)^(3/4) z])) + Sqrt[(-1)^(3/4) z]
((-(Pi/Sqrt[2])) (I Sqrt[2] E^(I Sqrt[2] z) z + (1 + I) (-1)^\[Nu]
E^(Sqrt[2] z) ((-2 + 2 I) Sqrt[2] z + Sqrt[(-I) z^2])) +
4 (E^(I Sqrt[2] z) z - (-1)^(3/4 + \[Nu]) E^(Sqrt[2] z)
Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z])))
HypergeometricPFQ[{(1 - 2 \[Nu])/8, (3 - 2 \[Nu])/8, (5 - 2 \[Nu])/8,
(7 - 2 \[Nu])/8, (1 + 2 \[Nu])/8, (3 + 2 \[Nu])/8, (5 + 2 \[Nu])/8,
(7 + 2 \[Nu])/8}, {1/4, 1/2, 3/4}, -(16/z^4)] -
(((-1)^(3/4) (1 - 4 \[Nu]^2))/(8 z))
(Sqrt[(-(-1)^(1/4)) z] (Pi (-4 (-1)^\[Nu] z - 3 I E^((1 + I) Sqrt[2] z)
z + 3 (-1)^(3/4 + \[Nu]) Sqrt[I z^2]) +
4 (E^((1 + I) Sqrt[2] z) z - (-1)^(1/4 + \[Nu]) Sqrt[I z^2])
(-Log[z] + Log[(-1)^(3/4) z])) + Sqrt[(-1)^(3/4) z]
((1/2) (-2 E^(I Sqrt[2] z) Pi z + (1 + I) (-1)^\[Nu] E^(Sqrt[2] z) Pi
((4 + 4 I) z - I Sqrt[2] Sqrt[(-I) z^2])) +
4 ((-I) E^(I Sqrt[2] z) z + (-1)^(1/4 + \[Nu]) E^(Sqrt[2] z)
Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z])))
HypergeometricPFQ[{(3 - 2 \[Nu])/8, (5 - 2 \[Nu])/8, (7 - 2 \[Nu])/8,
(9 - 2 \[Nu])/8, (3 + 2 \[Nu])/8, (5 + 2 \[Nu])/8, (7 + 2 \[Nu])/8,
(9 + 2 \[Nu])/8}, {1/2, 3/4, 5/4}, -(16/z^4)] +
((I (9 - 40 \[Nu]^2 + 16 \[Nu]^4))/(128 z^2))
((-Sqrt[(-(-1)^(1/4)) z]) (Pi (4 (-1)^\[Nu] z -
3 I E^((1 + I) Sqrt[2] z) z + ((3 - 3 I) (-1)^\[Nu] Sqrt[I z^2])/
Sqrt[2]) + 4 (E^((1 + I) Sqrt[2] z) z + (-1)^(1/4 + \[Nu])
Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z])) +
Sqrt[(-1)^(3/4) z] ((-(Pi/Sqrt[2])) (I Sqrt[2] E^(I Sqrt[2] z) z +
(1 + I) (-1)^\[Nu] E^(Sqrt[2] z) ((-2 + 2 I) Sqrt[2] z +
Sqrt[(-I) z^2])) + 4 (E^(I Sqrt[2] z) z - (-1)^(3/4 + \[Nu])
E^(Sqrt[2] z) Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z])))
HypergeometricPFQ[{(5 - 2 \[Nu])/8, (7 - 2 \[Nu])/8, (9 - 2 \[Nu])/8,
(11 - 2 \[Nu])/8, (5 + 2 \[Nu])/8, (7 + 2 \[Nu])/8, (9 + 2 \[Nu])/8,
(11 + 2 \[Nu])/8}, {3/4, 5/4, 3/2}, -(16/z^4)] -
(((-1)^(1/4) (-225 + 1036 \[Nu]^2 - 560 \[Nu]^4 + 64 \[Nu]^6))/
(3072 z^3)) ((-Sqrt[(-(-1)^(1/4)) z])
(Pi (-4 (-1)^\[Nu] z - 3 I E^((1 + I) Sqrt[2] z) z +
3 (-1)^(3/4 + \[Nu]) Sqrt[I z^2]) + 4 (E^((1 + I) Sqrt[2] z) z -
(-1)^(1/4 + \[Nu]) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z])) +
Sqrt[(-1)^(3/4) z] ((1/2) (-2 E^(I Sqrt[2] z) Pi z +
(1 + I) (-1)^\[Nu] E^(Sqrt[2] z) Pi ((4 + 4 I) z -
I Sqrt[2] Sqrt[(-I) z^2])) + 4 ((-I) E^(I Sqrt[2] z) z +
(-1)^(1/4 + \[Nu]) E^(Sqrt[2] z) Sqrt[(-I) z^2])
(-Log[z] + Log[(-(-1)^(1/4)) z]))) HypergeometricPFQ[
{(7 - 2 \[Nu])/8, (9 - 2 \[Nu])/8, (11 - 2 \[Nu])/8, (13 - 2 \[Nu])/8,
(7 + 2 \[Nu])/8, (9 + 2 \[Nu])/8, (11 + 2 \[Nu])/8, (13 + 2 \[Nu])/8},
{5/4, 3/2, 7/4}, -(16/z^4)]) /; (Abs[z] -> Infinity) &&
Element[\[Nu], Integers]
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<mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msqrt> <mrow> <mrow> <mo> - </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> <mo> ⁢ </mo> <mi> z </mi> 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</msup> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <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> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 8 </mn> </msub> <msub> <mi> F </mi> <mn> 3 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> 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5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 16 </mn> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], 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<mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mi> π </mi> <mtext> </mtext> </mrow> <msqrt> <mn> 2 </mn> </msqrt> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msqrt> <mrow> <mrow> <mo> - </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <msqrt> <mn> 2 </mn> </msqrt> </mfrac> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <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> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 8 </mn> </msub> <msub> <mi> F </mi> <mn> 3 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 16 </mn> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["11", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "5"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "7"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "9"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "11"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> </mrow> <mtext> </mtext> <mo> - </mo> <mrow> <mfrac> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msup> <mi> ν </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 560 </mn> <mo> ⁢ </mo> <msup> <mi> ν </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1036 </mn> <mo> ⁢ </mo> <msup> <mi> ν </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 225 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 3072 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <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> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msqrt> <mrow> <mrow> <mo> - </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <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> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 8 </mn> </msub> <msub> <mi> F </mi> <mn> 3 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 13 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 7 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 16 </mn> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", 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type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <pi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <imaginaryi /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> ν </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> ν </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 9 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 9 </cn> </apply> </apply> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 3 <sep /> 4 </cn> <cn type='rational'> 5 <sep /> 4 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <ci> ν </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <ci> ν </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 9 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 128 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> ν </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <pi /> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <imaginaryi /> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='complex-cartesian'> -2 <sep /> 2 </cn> <ci> z </ci> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <pi /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='complex-cartesian'> 3 <sep /> -3 </cn> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <imaginaryi /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> ν </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 9 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 11 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 11 </cn> </apply> </apply> </list> <list> <cn type='rational'> 3 <sep /> 4 </cn> <cn type='rational'> 5 <sep /> 4 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <power /> <ci> ν </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 560 </cn> <apply> <power /> <ci> ν </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1036 </cn> <apply> <power /> <ci> ν </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -225 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 3072 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <apply> <power /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <pi /> <apply> <plus /> <apply> <times /> <cn type='complex-cartesian'> 4 <sep /> 4 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <pi /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> ν </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <pi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <imaginaryi /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> ν </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> ν </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 9 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 11 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <cn type='integer'> 13 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <cn type='integer'> 13 </cn> </apply> </apply> </list> <list> <cn type='rational'> 5 <sep /> 4 </cn> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 7 <sep /> 4 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <ci> Rule </ci> <apply> <abs /> <ci> z </ci> </apply> <infinity /> </apply> <apply> <in /> <ci> ν </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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){kind=small}
