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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=-5/2, a2>=-5/2
For fixed z and a1=-5/2, a2=1, a3>=1
For fixed z and a1=-5/2, a2=1, a3=3
For fixed z and a1=-5/2, a2=1, a3=3, b1=-1/2
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http://functions.wolfram.com/07.27.03.abev.01
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HypergeometricPFQ[{-(5/2), 1, 3}, {-(1/2), 3/2}, -z] ==
-((7 (-112 + 1200 z + 450 Pi^2 z^(3/2) + 2700 z^2 + 675 Pi^2 z^(5/2)))/
1024) + (1/(6144 (1 + z)^(11/2)))
((-6144 + 57888 z + 851808 z^2 + 3649436 z^3 + 7805810 z^4 + 9519705 z^5 +
6752640 z^6 + 2604675 z^7 + 423810 z^8)
Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(6144 (1 + z)^(11/2)))
((6144 - 57888 z - 851808 z^2 - 3649436 z^3 - 7805810 z^4 - 9519705 z^5 -
6752640 z^6 - 2604675 z^7 - 423810 z^8)
Log[1 - Sqrt[z] + Sqrt[1 + z]]) -
(15 (-4 + 28 z + 315 z^2 + 315 z^3) Log[Sqrt[z] + Sqrt[1 + z]])/
(256 Sqrt[z] Sqrt[1 + z]) + (1/(6144 (1 + z)^(11/2)))
((6144 - 57888 z - 851808 z^2 - 3649436 z^3 - 7805810 z^4 - 9519705 z^5 -
6752640 z^6 - 2604675 z^7 - 423810 z^8)
Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) -
(1575/256) (2 z^(3/2) + 3 z^(5/2)) Log[Sqrt[z] + Sqrt[1 + z]]
Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])] -
(1575/256) (2 z^(3/2) + 3 z^(5/2))
PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] +
(1575/256) (2 z^(3/2) + 3 z^(5/2)) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["5", "2"]]], HypergeometricPFQ, 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HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1},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,...,ap},{b1,...,bq},z] | |
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