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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=-3/2
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http://functions.wolfram.com/07.27.03.abeg.01
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HypergeometricPFQ[{-(5/2), 1, 3}, {-(3/2), 5/2}, z] ==
-((3 I (-320 I + 672 I z + 1400 I z^2 + 6300 I z^3 + 1575 Pi^2 z^(7/2)))/
(4096 z)) + (15 Sqrt[1 - z] (-16 - 24 z - 42 z^2 - 105 z^3 + 315 z^4)
ArcSin[Sqrt[z]])/(1024 (-1 + z) z^(3/2)) -
(1/(49152 (-1 + z)^8)) (Sqrt[1 - z] (-11328 + 152800 z - 1035720 z^2 -
1677980 z^3 + 3809840 z^4 - 8712117 z^5 + 11826725 z^6 - 10083465 z^7 +
5306175 z^8 - 1581750 z^9 + 205020 z^10)
Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(49152 (-1 + z)^8))
(Sqrt[1 - z] (-11328 + 152800 z - 1035720 z^2 - 1677980 z^3 +
3809840 z^4 - 8712117 z^5 + 11826725 z^6 - 10083465 z^7 + 5306175 z^8 -
1581750 z^9 + 205020 z^10) Log[(1 - E^(I ArcSin[Sqrt[z]]))/
(1 + E^(I ArcSin[Sqrt[z]]))]) -
(4725 z^(5/2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/
(1 + E^(I ArcSin[Sqrt[z]]))])/1024 + (1/(49152 (-1 + z)^8))
(Sqrt[1 - z] (-11328 + 152800 z - 1035720 z^2 - 1677980 z^3 +
3809840 z^4 - 8712117 z^5 + 11826725 z^6 - 10083465 z^7 + 5306175 z^8 -
1581750 z^9 + 205020 z^10) Log[1 + E^(I ArcSin[Sqrt[z]])]) -
(4725 I z^(5/2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/1024 +
(4725 I z^(5/2) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/1024
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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> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 5 </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["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], 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</apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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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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