Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.9570)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=3, a₃>=3

For fixed z and a₁=-7/2, a₂=3, a₃=4

For fixed z and a₁=-7/2, a₂=3, a₃=4, b₁=5/2

http://functions.wolfram.com/07.27.03.9570.01

Input Form

HypergeometricPFQ[{-(7/2), 3, 4}, {5/2, 7/2}, z] == (1/(671088640 z^2)) (I (537600 I + 806400 Pi^2 Sqrt[z] + 9685760 I z + 15120000 Pi^2 z^(3/2) - 448820160 I z^2 - 176400000 Pi^2 z^(5/2) + 1511310528 I z^3 + 463050000 Pi^2 z^(7/2) - 1694939400 I z^4 - 458419500 Pi^2 z^(9/2) + 624323700 I z^5 + 156080925 Pi^2 z^(11/2))) - (1/(33554432 z^(5/2))) (21 Sqrt[1 - z] (-1280 - 15808 z - 388944 z^2 + 2292192 z^3 - 3374910 z^4 + 1486485 z^5) ArcSin[Sqrt[z]]) + (Sqrt[1 - z] (-108864000 + 419526577280 z + 732221853440 z^2 + 15633913538448 z^3 - 46318704099228 z^4 + 144372246608961 z^5 - 308697034120965 z^6 + 493898109798429 z^7 - 599597738566875 z^8 + 555206950722060 z^9 - 390341509193225 z^10 + 205172531210200 z^11 - 78204411159525 z^12 + 20439045290475 z^13 - 3279245548950 z^14 + 243720598275 z^15) Log[1 - E^(I ArcSin[Sqrt[z]])])/ (22649241600 (-1 + z)^11 z) + (Sqrt[1 - z] (108864000 - 419526577280 z - 732221853440 z^2 - 15633913538448 z^3 + 46318704099228 z^4 - 144372246608961 z^5 + 308697034120965 z^6 - 493898109798429 z^7 + 599597738566875 z^8 - 555206950722060 z^9 + 390341509193225 z^10 - 205172531210200 z^11 + 78204411159525 z^12 - 20439045290475 z^13 + 3279245548950 z^14 - 243720598275 z^15) Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))])/(22649241600 (-1 + z)^11 z) + (1/(33554432 z^(3/2))) (315 (512 + 9600 z - 112000 z^2 + 294000 z^3 - 291060 z^4 + 99099 z^5) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) - (Sqrt[1 - z] (-108864000 + 419526577280 z + 732221853440 z^2 + 15633913538448 z^3 - 46318704099228 z^4 + 144372246608961 z^5 - 308697034120965 z^6 + 493898109798429 z^7 - 599597738566875 z^8 + 555206950722060 z^9 - 390341509193225 z^10 + 205172531210200 z^11 - 78204411159525 z^12 + 20439045290475 z^13 - 3279245548950 z^14 + 243720598275 z^15) Log[1 + E^(I ArcSin[Sqrt[z]])])/ (22649241600 (-1 + z)^11 z) + (1/(33554432 z^(3/2))) (315 I (512 + 9600 z - 112000 z^2 + 294000 z^3 - 291060 z^4 + 99099 z^5) PolyLog[2, -E^(I ArcSin[Sqrt[z]])]) - (1/(33554432 z^(3/2))) (315 I (512 + 9600 z - 112000 z^2 + 294000 z^3 - 291060 z^4 + 99099 z^5) PolyLog[2, E^(I ArcSin[Sqrt[z]])])

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", "3", ",", "4"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["671088640", " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["537600", " ", "\[ImaginaryI]"]], "+", RowBox[List["806400", " ", SuperscriptBox["\[Pi]", "2"], " ", SqrtBox["z"]]], "+", RowBox[List["9685760", " ", "\[ImaginaryI]", " ", "z"]], "+", RowBox[List["15120000", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["448820160", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["176400000", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["1511310528", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["463050000", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["1694939400", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["458419500", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["624323700", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["156080925", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]]]], ")"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List["33554432", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], RowBox[List["21", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1280"]], "-", RowBox[List["15808", " ", "z"]], "-", RowBox[List["388944", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2292192", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["3374910", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1486485", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "108864000"]], "+", RowBox[List["419526577280", " ", "z"]], "+", RowBox[List["732221853440", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["15633913538448", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["46318704099228", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["144372246608961", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["308697034120965", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["493898109798429", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["599597738566875", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["555206950722060", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["390341509193225", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["205172531210200", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["78204411159525", " ", SuperscriptBox["z", "12"]]], "+", RowBox[List["20439045290475", " ", SuperscriptBox["z", "13"]]], "-", RowBox[List["3279245548950", " ", SuperscriptBox["z", "14"]]], "+", RowBox[List["243720598275", " ", SuperscriptBox["z", "15"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List["22649241600", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "11"], " ", "z"]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["108864000", "-", RowBox[List["419526577280", " ", "z"]], "-", RowBox[List["732221853440", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["15633913538448", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["46318704099228", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["144372246608961", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["308697034120965", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["493898109798429", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["599597738566875", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["555206950722060", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["390341509193225", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["205172531210200", " ", SuperscriptBox["z", "11"]]], "+", RowBox[List["78204411159525", " ", SuperscriptBox["z", "12"]]], "-", RowBox[List["20439045290475", " ", SuperscriptBox["z", "13"]]], "+", RowBox[List["3279245548950", " ", SuperscriptBox["z", "14"]]], "-", RowBox[List["243720598275", " ", SuperscriptBox["z", "15"]]]]], ")"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List["22649241600", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "11"], " ", "z"]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["33554432", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List["315", " ", RowBox[List["(", RowBox[List["512", "+", RowBox[List["9600", " ", "z"]], "-", RowBox[List["112000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["294000", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["291060", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["99099", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]], "]"]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "108864000"]], "+", RowBox[List["419526577280", " ", "z"]], "+", RowBox[List["732221853440", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["15633913538448", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["46318704099228", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["144372246608961", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["308697034120965", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["493898109798429", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["599597738566875", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["555206950722060", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["390341509193225", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["205172531210200", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["78204411159525", " ", SuperscriptBox["z", "12"]]], "+", RowBox[List["20439045290475", " ", SuperscriptBox["z", "13"]]], "-", RowBox[List["3279245548950", " ", SuperscriptBox["z", "14"]]], "+", RowBox[List["243720598275", " ", SuperscriptBox["z", "15"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List["22649241600", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "11"], " ", "z"]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["33554432", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], RowBox[List["315", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["512", "+", RowBox[List["9600", " ", "z"]], "-", RowBox[List["112000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["294000", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["291060", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["99099", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]]], "]"]]]]]], "-", RowBox[List[FractionBox["1", RowBox[List["33554432", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], RowBox[List["315", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["512", "+", RowBox[List["9600", " ", "z"]], "-", RowBox[List["112000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["294000", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["291060", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["99099", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]]]]]]]]]]

MathML Form

<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> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 3 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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[RowBox[List[TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "2"], 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] </annotation> </semantics> <mo>  </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 671088640 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 156080925 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 624323700 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 458419500 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1694939400 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 463050000 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1511310528 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 176400000 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 448820160 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 15120000 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9685760 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 806400 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <mrow> <mn> 537600 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 21 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1486485 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3374910 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2292192 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 388944 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 15808 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 1280 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 33554432 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 22649241600 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 11 </mn> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 243720598275 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 15 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3279245548950 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 14 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20439045290475 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 78204411159525 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 205172531210200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 390341509193225 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 555206950722060 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 599597738566875 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 493898109798429 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 308697034120965 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 144372246608961 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 46318704099228 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 15633913538448 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 732221853440 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 419526577280 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 108864000 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 22649241600 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 11 </mn> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 243720598275 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 15 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3279245548950 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 14 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 20439045290475 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 78204411159525 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 205172531210200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 390341509193225 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 555206950722060 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 599597738566875 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 493898109798429 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 308697034120965 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 144372246608961 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 46318704099228 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 15633913538448 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 732221853440 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 419526577280 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 108864000 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 33554432 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mn> 315 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 99099 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 291060 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 294000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 112000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9600 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 512 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 22649241600 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 11 </mn> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 243720598275 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 15 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3279245548950 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 14 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20439045290475 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 78204411159525 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 205172531210200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 390341509193225 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 555206950722060 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 599597738566875 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 493898109798429 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 308697034120965 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 144372246608961 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 46318704099228 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 15633913538448 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 732221853440 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 419526577280 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 108864000 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 315 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 99099 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 291060 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 294000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 112000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9600 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 512 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 33554432 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 315 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 99099 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 291060 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 294000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 112000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9600 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 512 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 33554432 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <cn type='integer'> 3 </cn> <cn type='integer'> 4 </cn> </list> <list> <cn type='rational'> 5 <sep /> 2 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 671088640 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 156080925 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 624323700 </cn> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 458419500 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1694939400 </cn> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 463050000 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1511310528 </cn> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 176400000 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 448820160 </cn> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15120000 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9685760 </cn> <imaginaryi /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 806400 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 537600 </cn> <imaginaryi /> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 21 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1486485 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3374910 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2292192 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 388944 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 15808 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1280 </cn> </apply> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 33554432 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 22649241600 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 11 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 243720598275 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 15 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3279245548950 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 14 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 20439045290475 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 13 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 78204411159525 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 205172531210200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 390341509193225 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 555206950722060 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 599597738566875 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 493898109798429 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 308697034120965 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 144372246608961 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 46318704099228 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15633913538448 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 732221853440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 419526577280 </cn> <ci> z </ci> </apply> <cn type='integer'> -108864000 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 22649241600 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 11 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -243720598275 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 15 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3279245548950 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 14 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 20439045290475 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 13 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 78204411159525 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 205172531210200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 390341509193225 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 555206950722060 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 599597738566875 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 493898109798429 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 308697034120965 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 144372246608961 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 46318704099228 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 15633913538448 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 732221853440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 419526577280 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 108864000 </cn> </apply> <apply> <ln /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 33554432 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 315 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 99099 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 291060 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 294000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 112000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9600 </cn> <ci> z </ci> </apply> <cn type='integer'> 512 </cn> </apply> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ln /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 22649241600 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 11 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 243720598275 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 15 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3279245548950 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 14 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 20439045290475 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 13 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 78204411159525 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 205172531210200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 390341509193225 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 555206950722060 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 599597738566875 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 493898109798429 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 308697034120965 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 144372246608961 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 46318704099228 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15633913538448 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 732221853440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 419526577280 </cn> <ci> z </ci> </apply> <cn type='integer'> -108864000 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 315 </cn> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 99099 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 291060 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 294000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 112000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9600 </cn> <ci> z </ci> </apply> <cn type='integer'> 512 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 33554432 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 315 </cn> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 99099 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 291060 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 294000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 112000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9600 </cn> <ci> z </ci> </apply> <cn type='integer'> 512 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 33554432 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", "3", ",", "4"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["537600", " ", "\[ImaginaryI]"]], "+", RowBox[List["806400", " ", SuperscriptBox["\[Pi]", "2"], " ", SqrtBox["z"]]], "+", RowBox[List["9685760", " ", "\[ImaginaryI]", " ", "z"]], "+", RowBox[List["15120000", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["448820160", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["176400000", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["1511310528", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["463050000", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["1694939400", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["458419500", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["624323700", " ", "\[ImaginaryI]", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["156080925", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]]]], ")"]]]], RowBox[List["671088640", " ", SuperscriptBox["z", "2"]]]], "-", FractionBox[RowBox[List["21", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1280"]], "-", RowBox[List["15808", " ", "z"]], "-", RowBox[List["388944", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2292192", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["3374910", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1486485", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]], RowBox[List["33554432", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "108864000"]], "+", RowBox[List["419526577280", " ", "z"]], "+", RowBox[List["732221853440", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["15633913538448", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["46318704099228", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["144372246608961", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["308697034120965", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["493898109798429", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["599597738566875", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["555206950722060", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["390341509193225", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["205172531210200", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["78204411159525", " ", SuperscriptBox["z", "12"]]], "+", RowBox[List["20439045290475", " ", SuperscriptBox["z", "13"]]], "-", RowBox[List["3279245548950", " ", SuperscriptBox["z", "14"]]], "+", RowBox[List["243720598275", " ", SuperscriptBox["z", "15"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["22649241600", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "11"], " ", "z"]]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["108864000", "-", RowBox[List["419526577280", " ", "z"]], "-", RowBox[List["732221853440", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["15633913538448", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["46318704099228", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["144372246608961", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["308697034120965", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["493898109798429", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["599597738566875", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["555206950722060", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["390341509193225", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["205172531210200", " ", SuperscriptBox["z", "11"]]], "+", RowBox[List["78204411159525", " ", SuperscriptBox["z", "12"]]], "-", RowBox[List["20439045290475", " ", SuperscriptBox["z", "13"]]], "+", RowBox[List["3279245548950", " ", SuperscriptBox["z", "14"]]], "-", RowBox[List["243720598275", " ", SuperscriptBox["z", "15"]]]]], ")"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]], "]"]]]], RowBox[List["22649241600", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "11"], " ", "z"]]], "+", FractionBox[RowBox[List["315", " ", RowBox[List["(", RowBox[List["512", "+", RowBox[List["9600", " ", "z"]], "-", RowBox[List["112000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["294000", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["291060", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["99099", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]], "]"]]]], RowBox[List["33554432", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "108864000"]], "+", RowBox[List["419526577280", " ", "z"]], "+", RowBox[List["732221853440", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["15633913538448", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["46318704099228", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["144372246608961", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["308697034120965", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["493898109798429", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["599597738566875", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["555206950722060", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["390341509193225", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["205172531210200", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["78204411159525", " ", SuperscriptBox["z", "12"]]], "+", RowBox[List["20439045290475", " ", SuperscriptBox["z", "13"]]], "-", RowBox[List["3279245548950", " ", SuperscriptBox["z", "14"]]], "+", RowBox[List["243720598275", " ", SuperscriptBox["z", "15"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["22649241600", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "11"], " ", "z"]]], "+", FractionBox[RowBox[List["315", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["512", "+", RowBox[List["9600", " ", "z"]], "-", RowBox[List["112000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["294000", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["291060", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["99099", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]]], "]"]]]], RowBox[List["33554432", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], "-", FractionBox[RowBox[List["315", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["512", "+", RowBox[List["9600", " ", "z"]], "-", RowBox[List["112000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["294000", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["291060", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["99099", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["33554432", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]]]]]]]

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

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},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,...,a_p},{b₁,...,b_q},z]